If x=\frac{\sqrt3-\sqrt2}{\sqrt3+\sqrt2} and y=\frac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2}, then the value of x^ 3 + y ^3 is:

Algebra and Applications Test 3

Question : 2 of 25

Marks: +1, -0

x={√3-√2}/{√3+√2}

and

y={√3+√2}/{√3-√2}

, then the value of

x^ 3 + y ^3

is:

Solution:

x={√3-√2}/{√3+√2}

={√3-√2}/{√3+√2}×{√3+√2}/{√3-√2}

=5-2√6

Similarly,

y={√3+√2}/{√3-√2}=5+2√6

Now,

x^3+y^3=(5-2√6)^3(5+2√6)^3

=125-48√6-30√6(5-2√6)

+125+48√6+30√6(5+2√6)

=970

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