Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

The number of real solution of the equation x^(2)-3|x|+2=0 is

The solution set of the equation x^(log_x(1-x)^2)=9 is

The number of distinct real roots of the equation sin pi x=x^(2)-x+(5)/(4) is

The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=-sqrt(3) is 4 (b) 5 (c) 6 (d) none of these

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

Number of solutions of the equation |2-|x||=x +4 is

The number of distinct real roots of the equation sin^(3)x +sin^(2)x sin x-sin x- sin 2x-2cos x=0 belonging to the interval (-(pi)/(2),(pi)/(2))

The number of distinct of real roots of the equation tan^(2)2x+2tan2x tan3x-1=0 in the interval [0,(pi)/(2)] is

The number of distinct real roots of the equation sqrt(sin x)-(1)/(sqrt(sin x))=cos x("where" 0le x le 2pi) is

The number of solution of the equation 2sin^(-1)((2x)/(1+x^(2)))-pi x^(3)=0 is equal to