find the value of
(2° +3-1 ) x 3
Answers
Answer:
What would you like to ask?
7th
Maths
Algebraic Expressions
Finding the Value of an Expression
If x = 2 - √(3), then find ...
MATHS
If x=2−
3
, then find the value of x
3
−1/x
3
EASY
Share
Study later
ANSWER
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
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
Mark as brainlist plzz plz hansika