Question

if x²+1/x²=1,then the value of x³+1/x³ is ? explain plz

Answer 1

Heya friend,
Here is the answer you were looking for:
${x}^{2} + \frac{1}{ {x}^{2} } = 1$

We can also write it as

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

Cubing both the sides we get

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

Using the identity :

${(a + b)}^{3} = {a}^{3} + {a}^{3} + 3ab(a + b)$

${(x)}^{3} + {( \frac{1}{x} )}^{3} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) = 1 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3(1) = 1 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + 3 = 1 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 1 - 3 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = - 2$


Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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