# Algebra Math Problem, x³ + 4x = 8, Then x⁷ + 64x² + 2 =?

If *x* be real number such that *x*³ + 4*x* = 8, find the value of *x*⁷ + 64*x*² + 2

## Solution to the algebra math problem

To solve the algebra math problem let

*x*³ + 4*x* = 8………………*eq*(1)

Square both sides, then

(*x*³ + 4*x*)² = 8²

*x*⁶ + 2 × *x*³ × 4*x* + (4*x*)² = 64

⇒ *x*⁶ + 8*x*⁴ + 16*x*² = 64

From equation 1, 8 – 2*x* = *x*³ + 2*x* , then

*x*⁶ + 8x(*x*³ + 2*x*) = 64

*x*⁶ + 8*x*(8 – 2*x*) = 64

* x*⁶

*+*64x – 16

*x*² = 64

Multiply with *x*

* x*⁷

*+*64x² – 16

*x*³ = 64

*x*

* x*⁷

*+*64x² = 64

*x*+ 16

*x*³

From equation 1, *x*³ = 8 – 4*x*, then

* x*⁷

*+*64x² = 64

*x*+ 16(8 – 4

*x*)

* x*⁷

*+*64x² = 64

*x*+ 128 – 64

*x*

* x*⁷

*+*64x² = 128

* x*⁷

*+*64x² + 2 = 128 + 2

* x*⁷ + 64x² + 2 = 130

So solution to the math problem is * x*⁷ + 64

*x*² + 2 = 130