Question

If x,y,z are in continued proportion prove-:.....Question is given in picture question no.20.....Thnk u

Answer 1

since , x , y , z are in continued proportion

hence , x : y :: y : z

=> x/y = y/z

=> y² = xz

LHS = (x+y)² / (y+z)²

=> (x²+y²+2xy) / (y²+z²+2yz)

=> (x²+xz+2xy) / (xz+z²+2yz). (as , y² = xz)


=> x (x+z+2y) / z (x+z+2y)

(x+z+2y) gets cancelled out


=> x / z

RHS = x / z


since , LHS = RHS

Proved


hope this helps