if X square + 1 by x square is equal to 83 then the value of x cube minus one by x cube is ?
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Hey Reshman,
x^2+1/x^2=83
=>(x^2)+(1/x^2)-2=83-2=81
=>x^2+1/x^2-2×x×1/x=81
=>(x-1/x)^2=9^2
=>x-1/x=9.
Now,x^3-1/x^3=(x-1/x)(x^2+1/x^2+x.1/x)
[Using formula
(a^3-b^3)=(a-b)(a^2+b^2+ab)]
=>x^3-1/x^3=(9)(83+1)=84×9=756.
Hope it helps
x^2+1/x^2=83
=>(x^2)+(1/x^2)-2=83-2=81
=>x^2+1/x^2-2×x×1/x=81
=>(x-1/x)^2=9^2
=>x-1/x=9.
Now,x^3-1/x^3=(x-1/x)(x^2+1/x^2+x.1/x)
[Using formula
(a^3-b^3)=(a-b)(a^2+b^2+ab)]
=>x^3-1/x^3=(9)(83+1)=84×9=756.
Hope it helps
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