Question

If x+√15=4 then x+1/x=?

Answer 1

x+$\sqrt{15}$=4

So, x=4-$\sqrt{15}$.......(1)

1/x=1/4-$\sqrt{15}$

=1/x=(1/4-$\sqrt{15}$)*(4+$\sqrt{15}$/4+$\sqrt{15}$)

=1/x=4+$\sqrt{15}$/4^2-15

=1/x=4+$\sqrt{15}$/16-15

=1/x=4+$\sqrt{15}$/1..........(2)

Adding (1) and (2):

x+1/x=4-$\sqrt{15}$+4+$\sqrt{15}$

=4+4=8

Hope you got your answer

Glad to help you.

Answer 2

You can solve this by substituting the value of x and then rationalising it