Question

X^2-15x+1=0 find x^4+1/x^4

Answer 1

Consider the given equation.

    x² - 15x + 1 = 0

Add 15x to both sides of the equation.

    x² - 15x + 1 + 15x = 0 + 15x

⇒  x² + 1 = 15x

Now, divide both sides by x.

    (x² + 1) / x  =  15x / x

⇒  x + 1/x  =  15

Square both sides of the equation.

    (x + 1/x)²  =  15²

⇒  x² + 1/x² + 2 = 225

Subtract 2 from both sides.

    x² + 1/x² = 223

Again square both sides of the equation.

    (x² + 1/x²)² = 223²

⇒  x⁴ + 1/x⁴ + 2 = 49729

Again subtract 2 from both sides, and thus we get,

    x⁴ + 1/x⁴ = 49727

Hence  49727  is the answer.