Question

if x+1/x=2 what is the value of x^3+1/x^3 can you please solve this with an explanation?.?.?.?.​ ?

Answer 1

Answer:

2

Step-by-step explanation:

(x+1/x)=2

seating both sides

(x+1/x)^2=4

x^2+1/x^2+2=4

x^2+1/x^2=2...........equ (1)

now (x^3+1/x^3)=(x+1/x) (x^2+1/x^2-1)

(x^3+1/x^3)=2×(2-1)=2 Ans

Answer 2

$x\:+\:\dfrac{1}{x}\:=\:2$

__________ [ GIVEN ]

• We have to find the value of ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }$

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→ $x\:+\:\dfrac{1}{x}\:=\:2$

Squaring on both sides

→ $\bigg(x\:+\:\dfrac{1}{x} \bigg)^{2} \: = \: ( {2)}^{2}$

(a + b)² = a² + b² + 2ab

→ ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: + \: 2x \: \times \: \dfrac{1}{x} \: = \: 4$

→ ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \: + \: 2\:=\:4$

→ ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \:=\:4\:-\:2$

→ ${x}^{2} \: + \: \dfrac{1}{ {x}^{2} } \:=\:2$

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Now..

→ ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }$ =

$\bigg (x \: + \: \dfrac{1}{x} \bigg) \: \bigg( {x}^{2} \: + \: \dfrac{1}{{x}^{2} } \: - \: x \: \times \: \dfrac{1}{x} \bigg)$

→ ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }$ =

$\bigg (x \: + \: \dfrac{1}{x} \bigg) \: \bigg( {x}^{2} \: + \: \dfrac{1}{{x}^{2} } \: - 1 \bigg)$

→ ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }\:=\:(2)\:(2\:-\:1)$ [From (eq 1)]

→ ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }\:=\:2(1)$

→ ${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }\:=\:2$

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${x}^{3} \: + \: \dfrac{1}{ {x}^{3} }\:=\:2$

________ [ ANSWER ]

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