Number of distinct real solutions of the equation `x^(2)+((x)/(x-1))^(2)=8` is (a) 1 (b) 2 (c)3 (d)4

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

`(c )` `x^(2)+((x)/(x-1))^(2)=8`
`implies (x+(x)/(x-1))^(2)-2x((x)/(x-1))=8`
`implies ((x^(2))/(x-1))^(2)-2((x^(2))/(x-1))-8=0`
`(x^(2))/(x-1)=timpliest^(2)-2t-8=0impliest=4`, `t=-2`
`(x^(2))/(x-1)=4impliesx^(2)-4x+4=0impliesx=2`
Put `(x^(2))/(x-1)=-2impliesx^(2)+2x=2implies(x+1)^(2)=3`
`implies x+1=+-sqrt(3)`
`implies x=+-sqrt(3)-1`