Question

if x+1/x=2,findx³+1/x³​

Answer 1

Step-by-step explanation:

Given:-

$x + \frac{1}{x} = 2$

To find:-

$\mathcal{The \: value \: \: \: of \: {x}^{3} + \frac{1}{ {x}^{3} } } =$

Solution:-

Let's solve the problem

We have,

$x + \frac{1}{x} = 2$

Cubing on both sides, we get

$⟹ \bigg(x + \frac{1}{x} \bigg)^{3} = (2 {)}^{3}$

⬤ Using algebraic identity:

[(a+b)³ = a³ + b³ + 3ab(a + b) ]

Now

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \cancel{x} \times \frac{1}{ \cancel{x}} \times \bigg(x + \frac{1}{x} \bigg) = 8$

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \bigg(x + \frac{1}{x} \bigg) = 8$

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 2 = 8$

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } + 6 = 8$

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } = 8 - 6$

$⟹ {x}^{3} + \frac{1}{ {x}^{3} } = 2$

Answer:-

$The \: value \: of \: {x}^{3} + \frac{1}{ {x}^{3} } \: is \: 2 .$

Used Formulae:

• (a+b)³ = a³+b³+3ab(a+b)