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

SSC CPO SI and ASI 2013 Paper

Question : 133 of 200

Marks: +1, -0

x= {√{3}-√{2}}/{√{3}+√{2}}

and

y=\ {√{3}+√{2}}/{√{3}-√{2}},

then the value of

x^{3}+y^{3}

Solution:

(4) (4) Here,

x= {√{3}-√{2}}/{\√{3}+√{2}} ×{√{3}-√{2}}/{√{3}-√{2}}

= {(√{3}-√{2})^{2}}/{3-2}=5-2 √{6}

y= {√{3}+√{2}}/{√{3}-√{2}} × {√{3}+√{2}}/{√{3}+√{2}}

= {(√{3}+√{2})^{2}}/{3-2}=5+2 √{6}

Hence,

x+y=10, x y=25-24=1

Now,the value of

x^{3}+y^{3}=(x+y)^{3}-3 x y(x+y)

=10^{3}-3 × 1 × 10

Hence,

x^{3}+y^{3}=10^{3}-30=970

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