Show that abc(abbcca)=abc Share with your friends Share Dear student Let ∆ = a a 3 a 4 1 b if a b c 6 and ab bc ca 11 find the value of a3 b3 c3 3abc Mathematics TopperLearningcom 3vrgnejoo Starting early can help you score better!A b c = 11, ab bc ca = 3 and abc = 135 As we know, a 3 b 3 c 3 – 3abc = (a b c) (a b c) 2 – 3(ab bc ca) ⇒ a 3 b 3 c 3 – 3 × (135) = 11 11 2 – 3 × 3 ⇒ a 3 b 3 c 3 405 = 11 × 121 – 9 = 11 × 112 ⇒ a 3 b 3 c 3 = 1232 – 405 = 7
Example 1 Construct A Triangle Abc In Which Angle B 60 C 45
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Notice, that in triangle ABC, that if we pick any point "P" on DG, then triangle APD will be congruent to triangle CPD by SAS Thus CP will be equal to AP But, for any point "P" that we select inside triangle CDG, then point "P" will be further from A and certainly further from BD, E and F are respectively the midpoints of sides AB, BC and CA of ∆ ABC Find the ratio of the areas of ∆ DEF and ∆ ABC Solution We know that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of it (midpoint theorem) According to the given question in ΔABC,In a triangle ABC, AB = BC = CA The ratio of the radius of the circumcircle to that of the incircle is A) 2 1 B) 3 1 C) 3 2 D) None of these Correct Answer A) 2
One way to arrive at the simplified expression is $ABA(\neg C)BC=AB(C(\neg C))A(\neg C)(B(\neg B))BC(A(\neg A))=ABCAB(\neg C)AB(\neg C)A(\neg B)(\neg C)ABC(\neg A)BC=ABCAB(\neg C)A(\neg B)(\neg C)(\neg A)BC=BC(A(\neg A))A(\neg C)(B(\neg B))=BCA(\neg C)$ $\endgroup$ – laissez_faire Sep 6 '16 at 1915Using properties of determinants, prove that 1a,1,1,1,1b,1,1,1,1c=abc bc ca ab= a 3 b 3 c 3 a 2 b a 2 b ac 2 ac 2 ab 2 ab 2 bc 2 bc 2 a 2 c a 2 c b 2 c b 2 c abc abc abc Above highlighted like terms will be subtracted and we get = a 3 b 3 c 3 abc abc abc Join like terms ie (abc) and we get = a 3 b 3 c 3 3abc Hence, in this way we obtain the identity ie a 3 b 3 c
Solution for abbcca=abc equation Simplifying ab bc ca = abc Reorder the terms ab ac bc = abc Solving ab ac bc = abc Solving for variable 'a' Move all terms containing a to the left, all other terms to the right Add '1abc' to each side of the equation ab ac 1abc bc = abc 1abc Reorder the terms ab 1abc ac bc = abc 1abc Combine like terms abc 1abc = 0 ab 1abc ac bc = 0 Add '1bc' to each side of the equation ab∠AEB = γ (given) ∴ ∠ABE = γ ∵ AE = AB Similarly ∠BDC = α given ∴ ∠BCD = α ∵ BC = BD Similarly ∠CFA = β given ∴ ∠FAC = β ∵ CFInteger solutions to abc = 2 (abbcca) WolframAlpha Rocket science?
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Uploaded By kana Pages 5 This preview shows page 4 5 out of 5 pagesΔabc की सभी भुजाएँ bc, ca और ab क्रमशः d, e और f पर एक वृत्त को स्पर्श करती है। तो af bd ce किसके बराबर है?Posted by Amit Kumar Sinha 2 days, 1 hour ago CBSE >
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Ex 102, 18 In triangle ABC (Fig 1018),which of the following is not true (A) (𝐴𝐵) ⃗ (𝐵𝐶) ⃗ (𝐶𝐴) ⃗= 0 ⃗ (B) (𝐴𝐵) ⃗ (𝐵𝐶 (a) Given, in two Δ ABC and Δ PQR, AB/QR = BC/PR = CA/PQ which shows that sides of one triangle are proportional to the side of the other triangle, then their corresponding angles are also equal, so by SSS similarity, triangles are similarJee main 21 1 vote 1 answer The number of rational terms in the binomial expansion of (4^1/45^1/6)^1 is _____
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(Consider the sides of triangles ∆ABM and ∆AMC)In ∆AMB, Sum of two sides > third side AB BM > AM In ∆AMC, Sum of two sides > third side CA CM > AM Adding (1) (2) AB BM CA CM > AM AM AB (BM CM) CA > 20045 ABC 'Home Economics' Premieres WEDNESDAY APRIL 7 on ABC!Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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If a b c = 6 and ab bc ca = 10, then value of a3 b3 c3 3abc is a) 36 b) 48 c) 42 d) 40Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries Students (upto class 102) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (MainsAdvance) and NEET can ask questions from any subject and get quick answers by1 Phân tích thành nhân tử (a b c)(ab bc ca)− abc ( a b c) ( a b b c c a) − a b c Theo dõi Vi phạm YOMEDIA Toán 8 Bài 6 Trắc nghiệm Toán 8 Bài 6 Giải bài tập Toán 8 Bài 6
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Example 1 Construct A Triangle Abc In Which Angle B 60 C 45
Given a b c = 2 ab bc ca = 2 abc = 2 Formula used (a b c)2 = a2 b2 c2 2(ab Q19 The distance between points P and Q is 485 km If a person starts from point P with the speed of 60 km/h and another person is running with a certain speed from point Q and they both meet after 25 hours then find the speed of the person who starts from point Q1cababcacabbc 1(1c)ab(1c)a(1c)b(1c) (1c)(1abab) 1 Thank You Sajal Agarwal 2 years, 4 months ago (1a)(1b)(1c) 1 Thank You ANSWER Related Questions 3root 5 by 2root 5 Report ;Simple and best practice solution for (abc)(bccaab)=9abc equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve it
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Draw a ∆ABC in which BC = 6 cm, CA=5cm and AB=4cm Construct triangle similar to it and of scale factor 5/3 asked in Constructions by Sima02 ( 493k points)BC = 7 và CA = 8 Số đo góc A bằng A 450 B 600 C 10 D 3000030 Rebel New Series 'Rebel' Coming to ABC on THURSDAY APRIL 8 See all the nominees, get the latest updates & watch LIVE Oscar Sunday, April 25 8e5p GO NOW >
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In a triangle ABC, AB BC = 12 cm, BC CA =14 cm and CA AB = 18 cm Find the radius of the circle (in cm) which has the same perimeter as the triangleएक त्रिभुज Δabc में, ∠abc और ∠acb के कोण You can see that if you expand (abc)^2, simplify, multiply by 2, and use the trivial inequality Instead of doing AMGM, I managed to solve it using CauchySchwartz Inequality There is likely a solution with AMGM, but I don't see it So here is mine (a 3 b 3 c 3 ) (abbcca) ≥abc (abc) 2 Divide all by abc
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L M and N lie on the sides AB BC and CA of the triangle ABC such that AL LB BM L m and n lie on the sides ab bc and ca of the School AlFarabi Kazakh National University;A 3 b 3 c 3 3abc = (a b c) (a 2 b 2 c 2 ab bc ca) Where a = 2a, b = 3b and c = 5c Now apply values of a, b and c on the LHS of identity ie a 3 b 3 c 3 3abc = (a b c) (a 2 b 2 c 2 ab bc ca) and we get = (2a 3b 5c) { (2a) 2 (3b) 2 (5c) 2 – (2a) (3b) – (3b) (5c) – (5c) (2a) }SolutionShow Solution As a, b, c, are in continued proportion Let `a/b = b/c` = k LHS = abc (a b c) 3 = ck 2 ckc ck 2 ck c 3 = c 3 k 3 c (k 2 k 1) 3 = c 3 k 3 c 3 (k 2 k 1) 3 = c6k 3 (k 2 k 1) 3 RHS = (ab bc ca) 3
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7 $\begingroup$ Set $\displaystyle abc=x$ So, we have $\displaystyle (xa)(xb)(xc)=x^3x^2(abc)(abbcca)xabc$ Now, $\displaystyle x^3x^2(abc)=x^2(x\overline{abc})=x^2\cdot0$ Share Cite Follow answered Jan '14 at 1605 Ex 64, 3 AM is a median of a triangle ABC Is AB BC CA > 2 AM?9OMO 14 Let ABC be a triangle with incenter I and AB = 1400, AC = 1800, BC = 14 The circle centered at I passing through A intersects line BC at two points X and Y Compute the length XY 10India RMO 14 Let ABC be an isosceles triangle with AB = AC and let denote its circumcircle A point D is on arc AB of not containing C
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Avail 25% off on study pack Avail OfferSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreWe can write ABCAB'CABC'= ABCAB'CABCABC' because for all X, XX=X in boolean algebra Then, since ABCAB'C=A (BB')C=AC and ABCABC'=AB (CC')=AB, the original expression becomes ACAB, which can also be written as A (CB) By the way, doing this using a Karnaugh map Wikipedia for three variables is simpler and faster!
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Tam giác ABC có AB = 5;If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, asked Mar 26 in Mathematics by MukeshKumar (319k points) jee;Maths NCERT Solutions Class 9 Chapter 9 Exercise 93 Question 5 Summary D, E, and F are respectively the midpoints of the sides BC, CA, and AB of triangle ABC, then BDEF is a parallelogram, Area of (DEF) = 1/4 Area of (ABC), and Area of (BDEF) = 1/2 Area of (ABC)
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D, E and F are respectively the midpoints of sides AB, BC and CA of ΔABC Find the ratio of the area of ΔDEF and ΔABC Get the answer to this question and access a vast question bank that is tailored for studentsCourse Title CHEM 2;In a triangle ABC which has its side AB = 30 mm along xaxis and In a triangle ABC which has its side AB = 30 mm along xaxis and side BC = 40 mm along yaxis Three forces of 50 N, 40 N and N act along the sides AB, BC and CA respectively The magnitude of the resultant of forces in Newton is Please scroll down to see the correct answer and solution guide
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Ab bc ca does not exceed aa bb cc Several proofs The inequality below, though simple, is useful and often comes up in proofs of more involved inequalities Given Triangle ABC in which D is a point on BC To prove AB BC CA > 2AD Construction AD is joined Proof In triangle ABD, AB BD > AD because, the sum of any two sides of a triangle is always greater than the third side 1 In triangle ADC, AC DC > AD because, the sum of any two sides of a triangle is always greater than theThe sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them Find the number of triangles that can be constructed using these points as vertices Find the number of triangles that can be constructed using these points as vertices
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