Question

if 2x+2/x=3 find equation x3+1/x3+2=?

Answer 1

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Answer 2

The value of $x^{3}+\dfrac{1}{x^{3}}+2=\dfrac{7}{8}.$

Step-by-step explanation:

We have,

$2x+\dfrac{2}{x} =3$

⇒ $2(x+\dfrac{1}{x}) =3$

⇒ $x+\dfrac{1}{x} =\dfrac{3}{2}$      ....(1)

To find, the value of $x^{3} +\dfrac{1}{x^{3}} +2$ =?

Cubing (1) in both sides, we get

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

⇒ $x^{3}+\dfrac{1}{x^{3}} +3x\frac{1}{x} (x+\frac{1}{x} ) =\dfrac{27}{8}$

⇒$x^{3}+\dfrac{1}{x^{3}} +3(\frac{3}{2} ) =\dfrac{27}{8}$

⇒$x^{3}+\dfrac{1}{x^{3}}+2=\dfrac{27}{8}-\dfrac{9}{2} +2$

⇒$x^{3}+\dfrac{1}{x^{3}}+2=\dfrac{27-36+16}{8}=\dfrac{43-36}{8}$

⇒$x^{3}+\dfrac{1}{x^{3}}+2=\dfrac{7}{8}$

Hence, the value of $x^{3}+\dfrac{1}{x^{3}}+2=\dfrac{7}{8}.$