JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q63

MathematicsSingle correct+4 / -1Question 63 of 90

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

−4

Answer and worked solution

Official answer: A

The power is 1 in three ways:

base 1: $x^2-5x+4=0$ , so $x=1,4$ ;
exponent 0 (base non-zero): $x^2+4x-60=0$ , so $x=6,-10$ ;
base −1 with an even exponent: $x^2-5x+6=0$ gives $x=2$ (exponent −48) or $x=3$ (exponent −39, odd, rejected).

The sum is $1+4+6-10+2=3$ .

JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 63