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Number of distinct real solutions of the...

Number of distinct real solutions of the equation `x^(2)+((x)/(x-1))^(2)=8` is

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
C
`(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`
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