Math, asked by nehrubhardwaj2180, 1 day ago

if x is 2+root3 then what is the value of X+1/X ?​

Answers

Answered by keshvipatel2311
1

Answer:

4

Step-by-step explanation:

x = 2 + root 3

x + 1/x = (2 + root 3) + (1/(2 + root 3))

= ( 2 + root 3 ) + (1/(2 + root 3) * (( 2 - root 3 ) / ( 2 + root 3 )) )

= (2 + root 3) + (( 2 + root 3 ) / 4 - 3)

= ( 2 + root 3 ) + ( 2 - root 3 )

= 4

Answered by jmlipika231
0

Step-by-step explanation:

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Question

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If x=2−

3

, then find the value of x

3

−1/x

3

Easy

Solution

verified

Verified by Toppr

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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