If x= \sqrt\sqrt{ 3 +1} /{\sqrt3 +1} , then what is the value of 3x^ 2 -( \sqrt2 +\sqrt3 )x ?

SSC CPO SI and ASI Model Paper 10

Question : 144 of 200

Marks: +1, -0

x= √√{ 3 +1} /{√3 +1}

, then what is the value of

3x^ 2 -( √2 +√3 )x

Solution:

(4)

x =√{√3 +1}/√{√3- 1}

=√ {{√3 +1}/{√ 3- 1}}[{√3- 1}/{ √3- 1}]

= √{{3- 1} /{3+1-2√ 3}}

x =√{1/{2-√3}}=√{2+√3}

[by rationalisation]

∴3x^2 - ( √{2 +√3 })x

=3(2 + √3) -(√ {2 +√3 })( √{2 +√3} )

=6 +3 √3 -2-√3 = 4 +2√ 3

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