Question

If
(a + 1/a)² = 3 and a € 0; then show that :

a³ + 1/a³= 0

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Answer 1

Answer:

Proven that, $a^3 + \frac{1}{a^3} = 0$

Step-by-step explanation:

Given that, $(a + \frac{1}{a} )^2 = 3$  and a ≠ 0

∴ $(a + \frac{1}{a} ) = \sqrt{3}$  . . . . . . . . . . . . . equation (i)

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

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

$= (\sqrt{3} )^3 - 3\sqrt{3}$  putting value from equation (i)

$= 3\sqrt{3} - 3\sqrt{3}$

= 0

Answer 2

Step-by-step explanation:

Here,

(a + 1/a)² = 3

or, a+1/a= (3)^1/2

or, a+1/a=9

Cubing on both sides

(a+1/a)^3= (3)^3/2

or, a^3+1/a^3+ 3*a*1/a(a+1/a) = (27)^1/2

or, a^3+ 1/a^3 + 3*3^1/2 = 3*3^1/2

i.e. a^3 + 1/a^3 = 0