Question

a+1/a=1,what is the valu of a^3+1​

Answer 1

Correct question says to find a³ + 1/a³

Answer:

- 2

Step-by-step-explanation :

Given,

→ a + 1/a = 1

Cube on both sides,

→ ( a + 1/a )³ = 1³

Using,

(a+b)³ = a³ + b³ + 3ab(a+b)

→ (a)³ + (1/a)³ + 3(a)(1/a)( a+1/a) = 1

→ a³ + 1/a³ + 3(1)(1) = 1

→ a³ + 1/a³ + 3 = 1

→ a³ + 1/a³ = 1 - 3

→ a³ + 1/a³ = - 2

Answer 2

Answer:

Given :-

$\frac{a \: + \: 1}{a} = \: 1$

To find :-

Value of

${a}^{3} + \frac{1}{a}^{3}$

Solution :-

We have given, $\frac{a \: + \: 1}{a} \: = 1$

By cubing both sides :-

${ (\frac{a \: + \: 1}{a}) }^{3} \: = \: {1}^{3}$

using Identity :-

${ (\frac{a \: + \: 1}{a}) }^{3} \: = {a}^{3} + {b}^{3} + 3ab(a+b)$

(a)³ + (1/a)³ + 3(a)(1/a)( a+1/a) = 1

a³ + 1/a³ + 3(1)(1) = 1

a³ + 1/a³ + 3 = 1

a³ + 1/a³ = 1 - 3

a³ + 1/a³ = - 2

Thus, Answer is (-2)