Sum of all real values of x satisfying equation {left( {{x^2} - 5x + 5} right)^{{x^2} + 4x - 60}} =

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4-2.Quadratic Equations and Inequations

hard

The sum of all real values of $x$ satisfying the equation ${\left( {{x^2} - 5x + 5} \right)^{{x^2} + 4x - 60}} = 1$ is ;

A

$6$

B

$5$

C

$3$

D

$-4$

(JEE MAIN-2016)

Solution

$x^{2}-5 x+5=1$

$\Rightarrow x=1,4$

$x^{2}-5 x+5=-1$

$\Rightarrow x=2,3$

but $3$ is rejected

$x^{2}+4 x-60=0$

$\Rightarrow x=-10,6$

$\operatorname{sum}=3$

Standard 11

Mathematics

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