Question

If (a + 1 /a )^2 = 9, then find the value of a^3+ 1 /a^3​

Answer 1

EXPLANATION.

⇒ (a + 1/a)² = 9.

As we know that,

We can write equation as,

⇒ (a + 1/a) = √9.

⇒ (a + 1/a) = 3.

As we know that,

Formula of :

⇒ (x + y)³ = x³ + 3x²y + 3xy² + y³.

Using this formula in equation, we get.

⇒ (a + 1/a)³ = (a)³ + 3(a)²(1/a) + 3(a)(1/a)² + (1/a)³.

⇒ (a + 1/a)³ = a³ + 3a + 3/a + 1/a³.

⇒ (a + 1/a)³ = a³ + 3(a + 1/a) + 1/a³.

Put the values in the equation, we get.

⇒ (3)³ = a³ + 3(3) + 1/a³.

⇒ 27 = a³ + 1/a³ + 9.

⇒ 27 - 9 = a³ + 1/a³.

⇒ 18 = a³ + 1/a³.

⇒ a³ + 1/a³ = 18.

Answer 2

Question

If (a + 1 /a )^2 = 9, then find the value of a^3+ 1 /a^3

To find

the value of a³+1/a³

Given

= (a+1/a)² = 9

= a+1/a = √9

= a+1/a = 3

= a³+1/a³ = ?

Now

= (a+1/a)³= 3³

$\sf {a}^{3} \: + \frac{1}{ {a}^{3} } + 3 \times \cancel{a} \times \frac{1}{ \cancel{a}} (a + \frac{1}{a} ) = 27$

a³+1/a² + 3 (3) = 27

a²+1a³ + 9 = 27

a³ + 1/a³ = 27 - 9

a³ + 1/a³ = 18