Home
Class 12
MATHS
The sum of values of x satisfying the eq...

The sum of values of `x` satisfying the equation `(31+8sqrt(15))^x^(2-3)+1=(32+8sqrt(15))^x^(2-3)` is `3` b. `0` c. `2` d. none of these

A

3

B

0

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
`(31 + 8sqrt(15))^(x^(2) - 3) + 1 = (32 + 8sqrt(15))^(x^(2) - 3)`
or `(31 + 8sqrt(15))^(x^(2) - 3) + 1^(x^(2) - 3) = (32 + 8sqrt(15))^(x^(2) - 3)`
`rArr x^(2) - 3 = 1` or `x = pm 2 " " [because a^(n) + b^(n) = (a + b)^(n)]`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.13|9 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

The values of x satisfying the equation (31+8sqrt(15))^(x^(2)-3)+1=(32+8sqrt(15))^(x^(2)-3)

The values of x satisfying the equation (31+8sqrt(15))^(x^(2)-3)+1=(32+8sqrt(15))^(x^(2)-3) is/are (A) 3 (B) 0 (C) 2 (D) -2

The values of x satisfying the equation (31+8sqrt(15))^(x^(2)-3)+1=(32+8sqrt(15) (A) 3 (B) 0 (C) 2 (D) -2

Number of values of x, satisfying the equation (sqrt(3)+1)^(2)x+(sqrt(3)-1)^(2)x=2^(3)x, is equal to

The number of values of x satisfying the equation log_(2)(log_(3)(log_(2)x)))>=sqrt(8-x)+sqrt(x-8) is :

The maximum value of x that satisfies the equation sin^(-1)((2sqrt(15))/(|x|))=cos^(-1)((14)/(|x|)) is

The value of x in (0,(pi)/(2)) satisfying the equation,(sqrt(3)-1)/(sin x)+(sqrt(3)+1)/(cos x)=4sqrt(2) is

The number of real solutions the equation sqrt(x+14-8sqrt(x-2))+sqrt(x+23-10sqrt(x-2))=3 are

Number of value(s) of 'x' which satisfy the equation log_(3+x^(2))(15+sqrt(x))=log_(5+x^(2))((1)/(2+sqrt(x))) is/are-

CENGAGE-THEORY OF EQUATIONS-Exercise (Single)
  1. The number of values of a for which equations x^3+a x+1=0 and x^4+a x^...

    Text Solution

    |

  2. The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1)...

    Text Solution

    |

  3. The sum of values of x satisfying the equation (31+8sqrt(15))^x^(2-3)+...

    Text Solution

    |

  4. The equation (x^2+x=1)^2+1=(x^2+x+1)(x^2-x-5) for x in (-2,3) will hav...

    Text Solution

    |

  5. If alpha,beta are the roots of x^2+p x+q=0a d nx^(2n)+p^n x^n+q^n=0a n...

    Text Solution

    |

  6. If P(x) is a polynomial with integer coefficients such that for 4 dist...

    Text Solution

    |

  7. Let f(x)=x^2+b x+c ,w h e r eb ,c in Rdot If f(x) is a factor of both...

    Text Solution

    |

  8. Consider the equation x^(2) + 2x - n = 0m where n in N and n in [5, 10...

    Text Solution

    |

  9. Number of integral values of a for which the equation x^2-(a+1)x+a-1=0...

    Text Solution

    |

  10. The number of integral values of a for which the quadratic equation (x...

    Text Solution

    |

  11. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

    Text Solution

    |

  12. The number of real solutions of |x|+2sqrt(5-4x-x^2)=16 is/are a. 6 ...

    Text Solution

    |

  13. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  14. If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^3+...

    Text Solution

    |

  15. If (mr ,1//mr),r=1,2,3,4, are four pairs of values of xa n dy that sat...

    Text Solution

    |

  16. If roots of an equation x^n-1=0 are 1,a1,a2,........,a(n-1) then the v...

    Text Solution

    |

  17. If tantheta1,tantheta2,tantheta3 are the real roots of the x^2-(a+1x^2...

    Text Solution

    |

  18. If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+...

    Text Solution

    |

  19. If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3K x^2...

    Text Solution

    |

  20. Set of all real value of a such that f(x)=((2a-1)+x^2+2(a+1)x+(2a-1))/...

    Text Solution

    |