If x^2 + 1/x^2 = 7, for x > 0, then the value of x + 1/x is

Answer 1

x^2 + 1/x^2 = 7 multiply by x^2

x^4 +1 = 7x^2. Let z=x^2

z^2 -7z + 1 = 0

z = 7/2 + or - (1/2)sqr(49-4)= 3.5+.5(3)sqr5= 3.5+ or - 1.5sqr5

x=+ or - sqr(3.5+ or -1.5sqr5) = about 2,62, -2.62, 0.38, -0.38

x+ 1/x = + or - sqr(3.5 + or -1.5sqr5) + 1/(+ or -sqr(3.5+ or -1.5sqr5)

= about 2.62 + 1/2.62 = 2.62+.38 = 3

or -2.62 -1/2.62 = -2.62-.38 = -3

or -.38 + 1/-.38 = -.38 -2.62 = -3

or .38 +1/.38 = 3

x+ 1/x = about 3 or -3