Question

9. If (a^2 + b^2) (x^2+ y^2) = (ax + by)^2;
prove that :
a/x = b/y​

Answer 1

Answer:

Given:

• (a²+b²)(x²+y²) = (ax+by)²

To Prove:

• a/x = b/y

Solution:

Multiplying the L.H.S,

• (a²+b²)(x²+y²) = a²x²+a²y²+b²x²+b²y²

Squaring the R.H.S,

• (ax+by)² = a²x²+2abxy+b²y²

Now, we know that L.H.S = R.H.S,

Hence,

a²x²+a²y²+b²x²+b²y² = a²x²+2abxy+b²y²

=> a²y²+b²x²–2abxy = 0

=> (ay–bx)² = 0

=> ay–bx = 0

=> ay = bx

=> a/x = b/y ...(proved)

Please mark it the BRAINLIEST