Question

if x+1/x = 4 then x^3+1/x^3 is?

Answer 1

Answer:

X + 1/X = 4

Cubing both sides ,

( X + 1/X )³ = (4)³

X³ + 1/X³ + 3 × X × 1/X × ( X + 1/X ) = 64

X³ + 1/X³ + 3 × 4 = 64

X³ + 1/X³ = 52

thank my answer ❤️

Answer 2

$\huge \mathfrak \red{answer}$

$\bf{ \boxed{ \underline{ \green{ \tt{ {x}^{ 3} = \frac{1}{x {}^{3} } = 52 \: }}}}}}}$

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$\sf \huge \underline {Given}$

$\rm{ \frac{x + 1}{x} = 4 \: then \: \frac{ {x}^{3} + 1 }{ {x}^{3}} }$

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$\sf \underline{step \: by \: step \: explanation}$

$\rm{x + \frac{1}{x} = 4}$

now cube on both sides we get,

$\sf \red{⟹ {x}^{3} - \frac{1}{x {}^{3} } + 3(x \times \frac{1}{x})(x + \frac{1}{x}) = 64}$

$\sf \blue{⟹ {x}^{3} + \frac{1}{x} {}{2} + 3(1)(4) = 64}$

$\sf \green{⟹ {x}^{3} + \frac{1}{x {}^{3} } = 64 - 12}$

$\sf \orange{⟹ {x}^{3} + \frac{1}{x {}^{3} } = 52}$

I hope it's help uh