Question

If x, y, z are in continued proportion then `(x^2 + y^2)/(y^2 + z^2)` is equal to ______.

पर्याय

• `x/z`

• `x/y`

• `y/z`

• `y/x`

Answer 1

If x, y, z are in continued proportion then `(x^2 + y^2)/(y^2 + z^2)` is equal to `bb(x/z)`.

Explanation:

If x, y, z are in continued proportion then,

`x/y = y/z`

y² = xz

Substitute y² = xz into the expression:

`(x^2 + y^2)/(y^2 + z^2)`

= `(x^2 + xz)/(xz + z^2)`

= `(x(x + z))/(z(x + z))`

= `x/z`