Question

If a+1/a=2 , find the value of a3+1/a3​

Answer 1

Given :-

• (a + 1/a) = 2

To Find :-

• (a³ + 1/a³) = ?

Solution :-

→ (a + 1/a) = 2

Cube Both sides we get,

→ (a + 1/a)³ = 2³

using (a+b)³ = a³ + b³ + 3ab(a+b) in LHS, we get,

→ a³ + 1/a³ + 3 * a * 1/a (a + 1/a) = 8

→ (a³ + 1/a³) + 3 * 2 = 8

→ (a³ + 1/a³) = 8 - 6

→ (a³ + 1/a³) = 2 . (Ans).

Hence, The value of (a³ + 1/a³) will also be 2.

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$</p><p>\tt{\green{Given \: - }}$

$\tt{ \purple{ = > a + \frac{1}{a} = 2 \: }}$

$\tt{ \red{ = >{( a + \frac{1}{a} )}^{3} = 8 \: }}$

$\tt{ \orange{ = > \: {a}^{3} + \frac{1}{ {a}^{3} } + 3a \frac{1}{a} (a + \frac{1}{a} ) = 8 \: }}$

$\tt{ \blue { = > {a}^{3} + \frac{1}{ {a}^{3} } + 3 \times 2 = 8 \: }}$

$\tt{ \green{ {a}^{3} + \frac{1}{ {a}^{3} } = 2} }$