Answer:
x1 = 8 ^ 1/2
x2 = - 8 ^ 1/2
x3 = 1
x4 = -1
Step-by-step explanation:
If our equation has the following form: x ^ 4 -9 * x + 8 = 0, it cannot be solved by substitution, but by factorization:
x ^ 4-9x + 8 = (x - 1) * (x ^ 3 + x ^ 2 + x - 8)
But if it has the form of x ^ 4 - 9x ^ 2 + 8 = 0, if you can:
let u = x ^ 2, then
u ^ 2 - 9 * u + 8 = 0
If we factor, two numbers that added to -9 but their multiplication is +8, would be -8, -1
- 8 - 1 = -9
- 8 * - 1 = 8
Thus:
(u - 8) * (u - 1) = 0
(u - 8) = 0 => u = 8
(u - 1) = 0 => u = 1
But we know that u is x ^ 2, therefore:
x ^ 2 = 8, x1 = 8 ^ 1/2; x2 = - 8 ^ 1/2
x ^ 2 = 1 x3 = 1, x4 = -1
