- Home
- Standard 11
- Mathematics
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