Question

Please solve number 9.

Answer 1

Hi ,

(a²+b²)(x²+y²)= (ax+by)²

a²(x²+y2)+ b²(x²+y2)= a²x²+2abxy +b² y²

a²x²+a² y²+b² x²+b² y²-a²x²-b² y²=2abxy

a²y²+ b² x²=2abxy

(ay)²+ ( bx)²-2×ay×bx=0

(ay - bx)²=0

ay-bx= 0

ay = bx

therefore,

a/x = b/y

hence proved.

I hope this helps you.

:)