Question

if x²+1/x²=7, then find the value of x³+1/x³​

a. 27
b. 9
c. 18
d. 36

Answer 1

EXPLANATION.

⇒ x² + 1/x² = 7.

As we know that,

We can write equation as,

⇒ (x + 1/x)² = x² + 1/x² + 2(x)(1/x).

⇒ (x + 1/x)² = x² + 1/x² + 2.

Put the values of x² + 1/x² = 7 in the equation, we get.

⇒ (x + 1/x)² = 7 + 2.

⇒ (x + 1/x)² = 9.

⇒ (x + 1/x) = √9.

⇒ (x + 1/x) = 3.

Cube on both sides of the equation, we get.

⇒ (x + 1/x)³ = (3)³.

As we know that,

Formula of :

⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³.

Using this formula in the equation, we get.

⇒ (x)³ + 3(x)²(1/x) + 3(x)(1/x)² + (1/x)³ = 27.

⇒ x³ + 3x + 3/x + 1/x³ = 27.

⇒ x³ + 1/x³ + 3x + 3/x = 27.

⇒ x³ + 1/x³ + 3(x + 1/x) = 27.

Put the value of x + 1/x = 3 in the equation, we get.

⇒ x³ + 1/x³ + 3(3) = 27.

⇒ x³ + 1/x³ + 9 = 27.

⇒ x³ + 1/x³ = 27 - 9.

⇒ x³ + 1/x³ = 18.

Option [C] is correct answer.

Answer 2

____________________________

★SOLUTION:-

(x + 1/x)2

x2 + 1/x2 + 2

(x + 1/x)2 = 9

x + 1/x = 3

Now,

(x + 1/x)3

x3 + 1/x3 + 3(x + 1/x)

27 = x3 + 1/x3 + 9

or,

x3 + 1/x3

27-9 = 18

$\therefore \textbf { \:(c) \: is \: the \: correct \: option }$

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