The sum of all real values of x satisfyi...

The sum of all real values of x satisfying the equation
`(x^(2) - 5x + 5 )^(x^(2 + 4x - 60)) = 1 ` is

A

3

B

-4

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:

B, D

We have, `(x^(2) - 4x + 5)^(x^(2)+4x-60) = 1`
`rArr" "x^(2) + 4x - 60 = 0 and x^(2) - 5x + 5 ne 0 or, x^(2)-5x + 5 = 1 and x^(2) = -10, 6 or, x = 1, 4`
`therefore" ""Required sum" = -10 + 6 = - 4 or, 1 + 4 = 5`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

QUADRATIC EXPRESSIONS AND EQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos
QUADRATIC EXPRESSIONS AND EQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|138 Videos
QUADRATIC EXPRESSIONS AND EQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos
PROBABILITY
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos
SEQUENCES AND SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

The sum of all real values of x satisfying the equation (x^(2) -5x+5)^(x^(2)+4x-45)=1 is :

Find the sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 .

The number of real values of x satisfying the equation 3 |x-2| +|1-5x|+4|3x+1|=13 is:

The set of all values of x satisfying the inequations |x-1| le 5 " and " |x|ge 2, is

Find the number or real values of x satisfying the equation 9^(2log_(9)x)+4x+3=0 .

The set of real values of x satisfying the equation |x-1|^(log_3(x^2)-2log_x(9))=(x-1)^7

Sum of all values of x satisfying the equation 25^(2x-x^2+1)+9^(2x-x^2+1)=34(15^(2x-x^2)) is:

The value of x satisfying the equation log_(2)(x^(2)-2x+5)=2 is "(a) 1 (b) 0 (c) -1 (d) 2 "

The value of x satisfying x^2 +5x + 6 = 0 is

If the sum of all values of y satisfying the equation e^y([x]-2)=[x]-1 where x in (3, 100) is S , then [S] is equal to

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Section I - Solved Mcqs

If alpha, beta are roots ................
Text Solution
|
If alpha,beta are the roots of the equation lamda(x^(2)-x)+x+5=0 and i...
Text Solution
|
If a in R and the equation (a-2) (x-[x])^(2) + 2(x-[x]) + a^(2) = 0 (w...
Text Solution
|
If all the roots of x^3 + px + q = 0 p,q in R,q != 0 are real, then
Text Solution
|
If three distinct real number a,b and c satisfy a^2(a+p)=b^2(b+p)=c^2(...
Text Solution
|
Let (sin a) x^(2) + (sin a) x + 1 - cos a = 0. The set of values of a ...
Text Solution
|
Let a and b are the roots of the equation x^2-10 xc -11d =0 and those...
Text Solution
|
Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...
Text Solution
|
Let a, b and c be three real numbers satisfying [a" "b" "c"][{:(1,9,7)...
Text Solution
|
The number of distinct real roots of x^4-4x^3+12 x 62+x-1=0i sdot
Text Solution
|
The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have on...
Text Solution
|
Let for a!=a(1)!=0f(x)=ax^(2)+bx+c, g(x)=a(1)x^(2)+b(1)x+c(1) and p(x)...
Text Solution
|
Sachin and Rahul attempted to solve a quadratic equation. Sachin made ...
Text Solution
|
Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...
Text Solution
|
The number of polynomials f(x) with non-negative integer coefficients ...
Text Solution
|
If a in R and the equation =-3(x-[x])^(2)+2(x-[x])+a^(2)=0 (where [x...
Text Solution
|
if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...
Text Solution
|
e^(|sin x|)+e^(-|sin x|)+4a=0 will have exactly four different solutio...
Text Solution
|
The sum of all real values of x satisfying the equation (x^(2) - 5...
Text Solution
|
Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...
Text Solution
|