If a/b=c/d then show (6a+7b)(3c-4d)=(6c+7d)(3a-4b)
Answers
Answered by
24
let,
a/b=c/d=k
it means, a=ck and b=dk
LHS,
(6a+7b)(3c-4d)
= {6×ck+7×dk}×{3×c-4×d}
=k×(6c+7d)×(3c-4d)
=k×(18c^2+21cd-24cd-28d^2)
=k(18c^2-3cd-28d^2)
RHS,
(6c+7d)(3a-4b)
=(6c+7d)(3×ck-4×dk)
=k×(18c^2+21cd-24cd-28d^2)
thus,
we can say,
LHS=RHS
a/b=c/d=k
it means, a=ck and b=dk
LHS,
(6a+7b)(3c-4d)
= {6×ck+7×dk}×{3×c-4×d}
=k×(6c+7d)×(3c-4d)
=k×(18c^2+21cd-24cd-28d^2)
=k(18c^2-3cd-28d^2)
RHS,
(6c+7d)(3a-4b)
=(6c+7d)(3×ck-4×dk)
=k×(18c^2+21cd-24cd-28d^2)
thus,
we can say,
LHS=RHS
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Answered by
8
Answer:
Given: a/b=c/d
Multiply both sides by 6/7;
=》6a/7b=6c/7d
=》(6a+7b)/7b=(6c+7d)/7d [BY COMPONENDO]
=》(6a+7b)/(6c+7d)=7b/7d=b/d...........1.
Again;
Multiply both sides by 3/4;
=》3a/4b=3c/4d
=》(3a-4b)/4b=(3c-4d)/4d [BY DIVIDENDO]
=》(3a-4b)/(3c-4d)=4b/4c=b/d............2.
Comparing equation 1. and 2.
=》(6a+7b)/(6c+7d)=(3a-4b)/(3c-4d)
=》(6a+7b)(3c-4d)=(6c+7d)(3a-4b)
Hence,proved...
Hope it helped you....
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