Question

if x+1/x=5,than x4+1/x2/x2-3x+1

Answer 1

Given:

x+1/x=5

To find:

x4+1/x2/x2-3x+1

Solution:

x + 1/x = 5

x² + 1 = 5x

squaring on both sides, we get,

(x² + 1)² = (5x)²

x⁴ + 1² + 2 × x² × 1 = 25x²

x⁴ + 1 + 2x² = 25x²

x⁴ + 1  = 23x²

x⁴ + 1 / x² - 3x + 1

= 23x² / x² - 3x + 1

= 23x² / x² + 1 - 3x

= 23x² / 5x - 3x

= 23x² / 2x

= 11.5x

Answer 2

Step-by-step explanation:

x+1/x =5 then [x^4+1/x^2]/(x^2-3x+1)=?

x^3+1/x^3

= (x+1/x)^3 - 3.x.1/x (x+1/x)

= (5)^3 - 3.5

110

[x^4+1/x^2]/(x^2-3x+1)

(Divide both numerator and denominator by x)

=(x^3+1/x^3)/ {(x+1/x)- 3}

=110/ (5-3)

=55