Question

IF A:B=C:D THEN PROVE A2+C2/AB+CD=AB+CD/B2+D2

Answer 1

Given :  A:B=C:D

To Find : Prove that

(A² + C²)/(AB + CD)  = (AB + CD)/(B² + D²)

Solution:

A:B=C:D

A/B = C/D = k

=> A = BK   and  C= DK

(A² + C²)/(AB + CD)  = (AB + CD)/(B² + D²)

LHS =

(A² + C²)/(AB + CD)

= ((BK)² + (DK)²)/(BKB + DKD)

= (K²(B² + D²)/K(B² + D²)

= K

RHS =

(AB + CD)/(B² + D²)

= (BKB + DKD)/(B² + D²)

= K(B² + D²)/(B² + D²)

= K

LHS = RHS = K

Hence  Proved (A² + C²)/(AB + CD)  = (AB + CD)/(B² + D²)

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