Question

If a=5+2√6 then find whether a-1/a is rational or irrational

Answer 1

If a=5+2√6 then a-1/a is a rational number;i.e; 0

Answer 2

Answer:

Step-by-step explanation:

GIVEN -- a=5+2$\sqrt{6}$ .......................(1)

TO PROVE -- a-1/a is rational or irrational

Proof --- a=5+2 $\sqrt{6$

             1/a = 1/5+2 $\sqrt{6$

 on  rationalising the denominator we get:

                 = 1/5+2$\sqrt{6$ *5-2$\sqrt{6$/5-2$\sqrt{6$

 therefore we get:

              =   5-2$\sqrt{6$ /($5^{2}$)-($2\sqrt{6} ^{2}$)

              =  5-2$\sqrt{6$/25-24

              =     5-2$\sqrt{6$/1......................(2)

on putting eq 1 and 2 in a-1/a we get:

              =   (5+2 $\sqrt{6$)-( 5-2$\sqrt{6$)

             i.e 0

            there  a-1/a is neither rational or irrational

hope this will help u