Question

If m =√2+1 ; find the value of
(m+1/m)3
​

Answer 1

(m+1/m)^3

m =√2+1

Then

(√2+1+1)/(√2+1)

= (√2+2)/(√2+1)

Rationalization

(√2+2)*(√2+1)/(√2+1)(√2-1)

= (2+√2+2√2+1)/(2-1)

= (3+3√2)

After cubing

(a+b)^3=a^2+3a^2b+3 ab^2+b^3

(3+3√2)^3 = 27+ 3*9*3√2 + 3*3*9*2 + 27*2

= 81+ 81√2 + 162

= 243 + 81√2

= 81 ( 3 + √2)