The number of integer solutions of the equation $$\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$$ i

Question

The number of integer solutions of the equation $$\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$$ is

Accepted Answer

Case 1: When x 2 − 3 x − 10 = 0 x^2-3x-10=0 x 2 − 3 x − 10 = 0 and x 2 − 10 ≠ 0 x^2-10
e\ 0 x 2 − 10  = 0 x^2-3x-10=0\ or, ( x − 5 ) ( x + 2 ) = 0 (x-5)(x+2) = 0 ( x − 5 ) ( x + 2 ) = 0 or, x= 5 or -2 Case 2: x 2 − 10 = 1 x^2-10=1 x 2 − 10 = 1 x 2 − 11 = 0 x^2-11=0 x 2 − 11 = 0 No integer solution

The number of integer solutions of the equation $\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$ is

The number of integer solutions of the equation $\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$ is

The number of integer solutions of the equation (x2−10)(x2−3x−10)=1\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1(x2−10)(x2−3x−10)=1 is

The number of integer solutions of the equation (x2−10)(x2−3x−10)=1\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1(x2−10)(x2−3x−10)=1 is

The number of integer solutions of the equation $\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$ is

The number of integer solutions of the equation $\left(x^{2} - 10\right)^{\left(x^{2}- 3x- 10\right)} = 1$ is