Question

If x-1/x= root 5 and x^2+1/x^2 find x+1/x

Answer 1

If x-1/x= root 5 and x^2+1/x^2 find x+1/x

x - 1/x = √5 ----( 1 )

i ) x² + 1/x² = ( x -1/x)² +2

= (√5)²+2

= 5+2

= 7

ii ) (x+1/x)² = (x-1/x)²+4

=(√5)²+4

= 5+4

=9

Now,

x+1/x = √(x+1/x )²

= √9

= ±3

Therefore ,

x²+1/x² = 7

x+1/x= ±3

••••