if x is 2+root3 then what is the value of X+1/X ?
Answers
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
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
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