Question

If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x²+ y² and y²+ z² 

Answer 1

Since y is the mean proportion between x and z 

Therefore, y²=xz 

Now, we have to prove that xy+yz is the mean proportional between x²+y² and y²+z². 

(xy + yz)² = (x² + y²)(y² + z²) 

LHS = (xy + yz)² 

= [y (x + z)]²

= y²(x + z)² 

= xz (x + z)²

RHS = (x² + y²)(y² + z²) 

= (x² + xz) (xz+ z²) 

= x (x + z) z (x + z)

= xz (x + z)²

LHS = RHS