SSC CHSL 6 Dec 2015 Shift 2 Paper

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Question : 109 of 200

Marks: +1, -0

If

a={√3-√2}/{√3+√2}

and

b={√3+√2}/{√3-√2}

, then the value of

a^2/b+b^2/a

is:

98
93
103
102

Solution:

Given :

a={√3-√2}/{√3+√2}

Rationalizing the denominator, we get :
⇒

a={√3-√2}/{√3+√2}×({√3-√2})/({√3-√2})

⇒

a=({√3-√2})^2/{({√3+√2})({√3-√2})}

⇒

a={3+2-2(√3)(√2)}/(3-2)

⇒

a = 5 − 2 √6

Similarly,

b = 5 + 2 √6

To find :

a^2+b^2

=

(5 − 2 √6)^2 + (5 + 2 √6)^2

=

(25 + 24 − 20 √6)

+ (25 + 24 + 20 √6)

=

49 + 49 = 98

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