Home
Class 12
MATHS
The set of real values of a for which th...

The set of real values of `a` for which the equation `(2a^(2)+x^(2))/(a^(3)-x^(3))-(2x)/(ax+a^(2)+x^(2))+(1)/(x-1)=0` has a unique solution is

A

`(-oo,1)`

B

`(-1,oo)`

C

`(-1,1)`

D

`R-{0}`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `(2a^(2)+x^(2))/(a^(3)-x^(3))-(2x)/(ax+a^(2)+x^(2))+(1)/(x-a) =0`
`implies (2x^(2)-3ax+a^(2))/(x^(3)-a^(3))=0 (x ne a)`
`implies 2x^(2)-3ax+a^(2)=0`
`implies x=a,(a)/(2)`
`:.(a)/(2)` is the only root if `(a)/(2) ne a`. ,brgt `:.a in (-oo,0)uu(0,oo)`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

Find the set of real values of 'm' for which the equation ((x)/(1+x^(2)))^(2)-(m-3)((x)/(1+x^(2)))+m=0 has real roots.

The values of 'a' for which the equation (x^(2)+x+2)^(2)-(a-3)(x^(2)+x+2)(x^(2)+x+1)+(a-4)(x^(2)+x+1)^(2)= has atlesast one real root is:

The complete set of real values of 'a' for which the equation 9^(x)-(4a)3^(x)+4-a^(2)=0 has a unique root is

The set of real values of x satisfying the equation |x-1|^(log_(3)(x^(2))-2log_(x)9)=(x-1)^(7)

Write the set of values of a'a' for which the equation x^(2)+ax-1=0 has real roots.

Solve the equation (2b^(2)+x^(2))/(b^(3)-x^(3))-(2x)/(bx+b^(2)+x^(2))+(1)/(x-b)=0 For what value of x is the solution of the equation unique ?

Complete set of real values of 'a' for which the equation x^(4)-2ax^(2)+x+a^(2)-a=0 has all its roots real

Complete set of real values of 'a' for which the equation x^(4)-2ax^(2)+x+a^(2)-a=0 has all its roots real:

Is there any real value of 'a' for which the equation x^(2)+2x+(a^(2)+1)=0 has real roots?

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