If x+1/x = 5 then!!!!!!!!!!!!!!!!!!!!!

Question

(x^4+1/x^2)/x^2-3x+1 = what?

Answer 1

Presumed [x+(1/x)]=5 then [x⁴+(1/x)⁴]/[x² - 3x + 1]=?

[x+(1/x)] = 5

Apply square each side.

[x+(1/x)]² = 5²

Mathematical formula: (a + b)² = a²+ 2ab + b²

x² + 2x(1/x)+(1/x)² = 25

x² + 2 + (1/x)² = 25

Subtract 2 from each side.

x² + (1/x)² = 23.

Again apply square each side.

[x² + (1/x)²]² = 23²

x⁴ + 2x²(1/x²)+1/x⁴ = 529

x⁴ + 2 + (1/x)⁴ = 529

Subtract 2 from each side.

x⁴ + (1/x)⁴ = 527----------->(1)

Take x+(1/x) = 5

Multiply each side by x.

x² + 1 = 5x.

Subtract 3x from each side.

x² + 1 - 3x = 2x----------(2)

Divide equation (1) and equation (2).

Therefore [x⁴+(1/x)⁴]/[x² - 3x + 1] = 527/(2x) = 263.5/x.