Question

if x= cube root of 2+ under root 3.find x power 3 +1/x power 3​

Answer 1

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

​