The sum of all the real values of x satisfyin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The equation $f(x)^{g(x)}=1$ is satisfied in the following cases:Case $1$: $f(x)=1$$x^2-7x+11=1 \implies x^2-7x+10=0 \implies (x-2)(x-5)=0 \implie

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(D) The equation $f(x)^{g(x)}=1$ is satisfied in the following cases:Case $1$: $f(x)=1$$x^2-7x+11=1 \implies x^2-7x+10=0 \implies (x-2)(x-5)=0 \implies x=2, 5$.Case $2$: $g(x)=0$ and $f(x) 
eq 0$$x^2-6x-7=0 \implies (x-7)(x+1)=0 \implies x=7, -1$.Case $3$: $f(x)=-1$ and $g(x)$ is an even integer$x^2-7x+11=-1 \implies x^2-7x+12=0 \implies (x-3)(x-4)=0 \implies x=3, 4$.Check $g(x)$ for $x=3, 4$:For $x=3$,$g(3)=3^2-6(3)-7=9-18-7=-16$ (even,so $x=3$ is a solution).For $x=4$,$g(4)=4^2-6(4)-7=16-24-7=-15$ (odd,so $x=4$ is not a solution).The set of real values of $x$ is $\{2, 5, 7, -1, 3\}$.The sum of these values is $2+5+7-1+3=16$.

The sum of all the real values of $x$ satisfying the equation $(x^2-7x+11)^{x^2-6x-7}=1$ is

Similar Questions

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

For which real value of $a$ do the roots of the quadratic equation $2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0$ have opposite signs?

For what values of $a \in \mathbb{Z}$,the quadratic expression $(x+a)(x+1991)+1$ can be factorised as $(x+b)(x+c)$,where $b, c \in \mathbb{Z}$?

Let $E$ denote the set of all integers $a$ such that the point of intersection of the parabola $y = x^2 + 2ax + 2021$ with the $x$-axis has rational coordinates. The largest element of $E$ is

The roots of the equation $a(b-c)x^2 + b(c-a)x + c(a-b) = 0$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module