Question

If a = root2+1 and b = 1/a .find the value of a^2 + b^2
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Answer 1

QUESTION :

If a = root2+1 and b = 1/a .find the value of a^2 + b^2

If a = root2+1 and b = 1/a .find the value of a^2 + b^2

ANSWER :

Given,

a = √2 + 1

b = 1/a = 1/(√2 + 1)

a^2 + b^2 = (√2 + 1 )^2 + 1/(√2 + 1 )^2

= 2 + 1 + 2(√2)(1) + (1/(2 + 1 + 2(√2)(1)))

= 3 + 2√2 + 1/(3 + 2√2)

By taking LCM :

= (9 + 8 + 2(3)(2√2) + 1 )/ 3 + 2√2

= (18 + 12√2)/ 3 + 2√2

FINAL ANSWER : (18 + 12√2)/ 3 + 2√2