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If x= 2 + 3, Find (x+1/x)3 |
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Answer» Step-by-step EXPLANATION: It is given that, x=2− 3
so, 1/x=1/(2− 3
) By rationalizing the denominator, we get =[1(2+ 3
)]/[(2− 3
)(2+ 3
)] =[(2+ 3
)]/[(2 2 )−( 3
) 2 ] =[(2+ 3
)]/[4−3] =2+ 3
Now, x−1/x=2− 3
−2− 3
=−2 3
Let us cube on both SIDES, we get (x−1/x) 3 =(−2 3
) 3
x 3 −1/x 3 −3(x)(1/x)(x−1/x)=24 3
x 3 −1/x 3 −3(−2/ 3
)=−24 3
x 3 −1/x 3 +6 3
=−24 3
x 3 −1/x 3 +6 3
=−24 3
x 3 −1/x 3 =−24 3
−6 3
=−30 3
Hence, x 3 −1/x 3 =−30 3
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