Find all real numbers x which satisfy the equation. 10x6−10x2=0

Answer 1

Factor

10x⁶ - 10x² = 10x²(x⁴ - 1) = 10x²(x² - 1)(x² + 1) = 10x²(x - 1)(x + 1)(x² + 1)

Then 10x⁶ - 10x² = 0 if and only if 10x²(x - 1)(x + 1)(x² + 1) = 0. Since x² + 1 has no real roots, 10x²(x - 1)(x + 1) = 0. Therefore x = 0, 1, or -1.

Answer 2

10x^6 - 10x^2 = 0

divide by 10

x^6 -x^2 = 0

factor out x^2

x^2(x^4-1) = 0

x^2(x^2-1)(x^2+1) = 0

x^2(x+1)(x-1)(x^2+1)

roots=solutions= 0, -1, +1, and i & -i