X= 2^1/3+2^-1/3; then find the value of 2X^3-6
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If x=2+2
2/3
+2
1/3
, then the value of x
3
−6x
2
+6x is
Medium
Solution
verified
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Correct option is B)
Given, x=2+2
2/3
+2
1/3
⇒(x−2)=2
2/3
+2
1/3
⇒(x−2)=2
2/3
+2
1/3
On cubing both sides, we get
(x−2)
3
=2
2
+2+3⋅2
2/3
⋅2
1/3
(2
2/3
+2
1/3
)
⇒x
3
−6x
2
+12x−8=4+2+3×2×(x−2)
⇒x
3
−6x
2
+6x=2.
Answered by
0
Given,
X = 2^ + 2^
To Find,
The value of 2X³- 6
Solution,
X = 2^ + 2^
On cubing both the sides, we get
⇒ (X)³ = (2^ + 2^
)³
⇒ (X)³ = 2 - 2 + 3 × 2^ × 2^
( 2^
+ 2^
)
⇒ (X)³ = 0 + 3 × 2⁰ (X)
⇒ (X)³ = 3X
⇒ X = √3
⇒ X = 1.732
∴ Substituting the value of X in the finding value,
⇒ 2X³- 6
⇒ 2 × (1.732)³ - 6
⇒ 2 × 5.189 - 6
⇒ 10.378 - 6
⇒ 4.378
Hence, the value of 2X³- 6 is 4.378
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