Question

x+1/x=4 then x^ +1/x^ is equal to
a) 12
b) 14
c) 16
d) 18

Answer 1

Answer:

Multiply both sides by x (check that x is not equal to 0 at the end as it would make the 1/x undefined)

x^2 + 1 = 4x

subtract 4x from both sides of the equation.

x^2 -4x + 1 = 0

Use the quadratic formula

x = (-(-4) +/- radical( (-4)^2 - 4*1*1) )/(2*1)

x = ( 4 +/- radical(12) )/2

x = ( 4 +/- 2*radical(3) )/2

x = 2 +/- radical(3)