We can rearrange the equation to have a quadratic expression:
x⁴ - 625x² = 0
Factoring out x², we have:
x²(x² - 625) = 0
Using the difference of squares (a² - b² = (a+b)(a-b)) with a = x and b = 25:
x²(x+25)(x-25) = 0
This gives us three possible values for x: x=0, x=25, and x=-25.
However, we need to check which values actually satisfy the original equation:
For x=0:
x⁴ = 0 and 625x² = 0, which means that x=0 satisfies the equation.
For x=25:
x⁴ = 390625 and 625x² = 390625, which means that x=25 also satisfies the equation.
For x=-25:
x⁴ = 390625 but 625x² = 390625*(-1), which means that x=-25 does not satisfy the equation.
Therefore, the solutions for x are x=0 and x=25.
If x⁴=625x² what is x?
1 answer
1 answer