Question

a+1/a=2 then a^(3)+1/a^(4)=?

Answer 1

Answer:

2

Step-by-step explanation:

Appropriate Question :

If  $\mathrm{a + \dfrac{1}{a} = 2}$ then, $\mathrm{a^3+\dfrac{1}{a^3}}$ = ?

Solution :

Given that,

$\longmapsto \mathrm{a + \dfrac{1}{a} = 2}$

Cubing that on both sides,

we know that,

$\boxed{\mathrm{(x+y)^3 = x^3+3x^2y+3xy^2+y^3}}$

Here, x = a ; y = 1/a

$\implies \mathrm{\bigg(a + \dfrac{1}{a}\bigg)^3 = 2^3}$

$\implies \mathrm{a^3+3a^{\not2}.\dfrac{1}{\not a} + 3\not a.\dfrac{1}{a^{\not 2}} + \dfrac{1}{a^3} = 8}$

$\implies \mathrm{a^3 + 3\bigg(a + \dfrac{1}{a}\bigg)+\dfrac{1}{a^3} = 8}$

As it is given, $\mathrm{a + \dfrac{1}{a} = 2}$

Substituting that, we get,

$\implies \mathrm{a^3 + 3(2)+\dfrac{1}{a^3} = 8}$

$\implies \mathrm{a^3 +\dfrac{1}{a^3} = 8-6}$

$\implies \mathrm{a^3+\dfrac{1}{a^3} = 2}$

Thus,

$\bigg|\overline{\underline{\boxed{\mathbf{a^3 + \dfrac{1}{a^3} = 2}}}}\bigg|$

Hope it helps!!