Question : If $\mathrm{y}+\frac{1}{\mathrm{y}}=3$, then what is the value of $\frac{1}{\mathrm{y}^3}+\mathrm{y}^3+2$ ?
Option 1: 24
Option 2: 18
Option 3: 20
Option 4: 29

Question

Question : If $\mathrm{y}+\frac{1}{\mathrm{y}}=3$, then what is the value of $\frac{1}{\mathrm{y}^3}+\mathrm{y}^3+2$ ?

Option 1: 24

Option 2: 18

Option 3: 20

Option 4: 29

Team Careers360 · Accepted Answer

Correct Answer: 20

Solution : Given, $\mathrm{y}+\frac{1}{\mathrm{y}}=3$
Cubing both sides, we get
⇒ $(\mathrm{y}+\frac{1}{\mathrm{y}})^3=3^3$
⇒ $\mathrm{y^3}+\frac{1}{\mathrm{y^3}}+3 imes\mathrm{y} imes\frac{1}{\mathrm{y}} imes(\mathrm{y}+\frac{1}{\mathrm{y}})=27$
⇒ $\mathrm{y^3}+\frac{1}{\mathrm{y^3}}+3(3)=27$
⇒ $\mathrm{y^3}+\frac{1}{\mathrm{y^3}}+9=27$
⇒ $\mathrm{y^3}+\frac{1}{\mathrm{y^3}}+2=27-7$
⇒ $\mathrm{y^3}+\frac{1}{\mathrm{y^3}}+2=20$
Hence, the correct answer is 20.

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Question : If y+1y=3, then what is the value of 1y3+y3+2 ?Option 1: 24Option 2: 18Option 3: 20Option 4: 29

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Question : If $y + \frac{1}{y} = 3$ , then what is the value of $\frac{1}{y^{3}} + y^{3} + 2$ ?
Option 1: 24
Option 2: 18
Option 3: 20
Option 4: 29