Algebra Math Problem, x³ + 4x = 8, Then x⁷ + 64x² + 2 =?
If x be real number such that x³ + 4x = 8, find the value of x⁷ + 64x² + 2
Solution to the algebra math problem
To solve the algebra math problem let
x³ + 4x = 8………………eq(1)
Square both sides, then
(x³ + 4x)² = 8²
x⁶ + 2 × x³ × 4x + (4x)² = 64
⇒ x⁶ + 8x⁴ + 16x² = 64
From equation 1, 8 – 2x = x³ + 2x , then
x⁶ + 8x(x³ + 2x) = 64
x⁶ + 8x(8 – 2x) = 64
x⁶ + 64x – 16x² = 64
Multiply with x
x⁷ + 64x² – 16x³ = 64x
x⁷ + 64x² = 64x + 16x³
From equation 1, x³ = 8 – 4x, then
x⁷ + 64x² = 64x + 16(8 – 4x)
x⁷ + 64x² = 64x + 128 – 64x
x⁷ + 64x² = 128
x⁷ + 64x² + 2 = 128 + 2
x⁷ + 64x² + 2 = 130
So solution to the math problem is x⁷ + 64x² + 2 = 130