Question

If x = 2√3 +2√2 , find :
(ii) 1/x ​

Answer 1

Given that :

x = 2√3 + 2√2

To find :

(1) 1/x

1/(2√3+2√2)

Rationalization :

1/x = 1/(2√3+2√2) × (2√3-2√2)/(2√3-2√2)

=> 1/x = 2(√3-√2)/{(2√3)^2-(2√2)^2

=> 1/x = 2(√3-√2)/12-8 = (√3-√2)/2

(2) x+1/x

=> (2√3+2√2)+(√3-√2)/2

=> (4√3+4√2+√3-√2)/2

=> (5√3+3√2)/2

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