Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201823 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In A B C , a^3 (B-C)+b^3 (C-A)+c^3 (A-B)=

Options

  1. Aa b c
  2. Ba + b + c
  3. C2 abc
  4. D3 abc

Correct answer

D. 3 abc

Step-by-step solution

In aligned & A B C, a^3 (B-C) & =a^3 ( 2 (B+C) (B-C) 2 (B+C) ) & =a^3 ( 2 B+ 2 C) 2 (B+C) ) & =a^3 ( 2 B B+2 c C 2 ( -A) ) & =a^3 ( B B+ C C A ) & =a^3 ( b k B+c K C a k ) aligned Adding Eqs. (i), (ii) and (iii), we get aligned & a^3 (B-C)+b^3 (C-A)+c^3 (A-B) & =a^2 b B+a^2 c C+b^2 c C & +b^2 a A+c^2 a A+c^2 b B & =a b(a B+b A)+a c(a C+c A) & =a b c+a b c+a b c=3 a b c +b c(b C+c B) aligned

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All AP EAMCET PYQs