If `b-c`, `bx-cy`, `bx^(2)-cy^(2)` (`b,c ne 0`) are in `G.P`, then the value of `((bx+cy)/(b+c))((bx-cy)/(b-c))` is

Options

A. `x^(2)`
B. `-x^(2)`
C. `2y^(2)`
D. `3y^(2)`

Answer

A

Explanation

`(a)` `(bx-cy)^(2)=(b-c)(bx^(2)-cy^(2))`
`b^(2)x^(2)+c^(2)y^(2)-2bxy=b^(2)x^(2)-bcy^(2)-bcx^(2)+c^(2)y^(2)`
`bcx^(2)+bcy^(2)-2bcxy=0`
`bc(x-y)^(2)=0`
`impliesx=y` (`:'b`, `c ne 0`)
`implies((bx+cy)/(b+c))((bx-cy)/(b-c))=x^(2)`