Question

find the value of
a^2 +b^2.

Answer 1

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Answer 2

a = ( √ 3 + √2)/ ( √ 3- √2)
after rationalisation of denominator we get, ( √ 3 + √2) ( √ 3 + √2) / ( √ 3- √2) ( √ 3 + √2)
= ( 3 +2 +2 √ 6)/ ( 3 -2)
=5 +2 √ 6 =a
so a ^ 2 = (5 +2 √ 6) ^ 2
=25 +24 +20 √ 6
=49 +20 √ 6

b = ( √ 3 - √2)/ ( √ 3 + √2)
after rationalisation of denominator,
( √ 3 - √2) ( √ 3- √2)/ ( √ 3 + √2) ( √ 3 - √2)
= ( 3 +2-2 √ 6)/ ( 3 -2)
=5 -2 √ 6 =b

b ^ 2 = (5 -2 √ 6) ^ 2
=25 +24 -20 √ 6
=49 -20 √ 6


a ^ 2 +b ^ 2
=49 +20 √ 6 +49 -20 √ 6
=49 +49
=98.


I hope it will help you.