If x-\sqrt{3}-\sqrt{2}=0 and y=\sqrt{3}+\sqrt{2}=0, then the value of (x^{3}-20 \sqrt{2} )- (y^{3}+20 \sqrt{2} )is

SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 83 of 100

Marks: +1, -0

x-√{3}-√{2}=0

and

y=√{3}+√{2}=0,

then the value of

(x^{3}-20 √{2} )- (y^{3}+20 √{2} )

Solution:

(1)

x-√{3}-√{2}=0

⇒ x=√{3}+√{2}

Again,

y-√{3}+√{2}=0

⇒ y=√{3}-√{2}

∴ x-y=√{3}+√{2}-√{3}+√{2} =2 √{2}

and

x y=(√{3}+√{2})(√{3}-√{2})

=3-2=1

∴ Expression

=x^{3}-20 √{2}-y^{3}-2 √{2}

=x^{3}-y^{3}-22√{2}

=(x-y)^{3}+3 x y(x-y)-22 √{2}

=(2 √{2})^{3}+3(2 √{2})-22 √{2}

=16 √{2}+6 √{2}-22 √{2}=0

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