Question

$x + \frac{1}{x} = 4 \: \: \: \: find \: x ^{3} + \frac{1}{x ^{3} }$
with full explanation​

Answer 1

x+1/x=4

(x+1/x)³=x³+1/x³+3*x*1/x(x+1/x)

4³=x³+1/x³+3*4

64-12=x³+1/x³

x³+1/x³=52

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Answer 2

Answer:-

Given:

x + 1/x = 4

Cubing both sides we get,

(x + 1/x)³ = (4)³

We know that,

(a + b)³ = a³ + b³ + 3ab (a + b)

So,

x³ + (1/x)³ + 3x * 1/x ( x + 1/x) = 64

→ x³ + 1/x³ + 3(1)(4) = 64

→ x³ + 1/x³ + 12 = 64

→ x³ + 1/x³ = 64 - 12

→ x³ + 1/x³ = 52