If x = \sqrt3+\sqrt 2, then the value of x^3-1/x^3 is:

Algebra and Applications Test 1

Question : 40 of 40

Marks: +1, -0

x = √3+√ 2

, then the value of

x^3-1/x^3

is:

Solution:

x = √3+√ 2

1/x=1/{√3+√2}=√3-√2

x-1/x=√3+√2-√3+√2

=2√2

Cubing both sides we get

x^3-1/x^3-3(x-1/x)=16√2

x^3-1/x^3-3(2√2)=16√2

x^3-1/x^3 =16√2+6√2=22√2

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