Question

. If ²+ 1/²= 27, then find
(i) − 1 / ,
(ii) ³ − 1 /³​

Answer 1

Answer:

Final Answer :±36

Steps :

1)

\begin{gathered} {x}^{2} + \frac{1}{ {x}^{2} } = 11 \\ = > {(x - \frac{1}{x} )}^{2} + 2 = 11 \\ = > {(x - \frac{1}{x} )}^{2} = 11 - 2 = 9 \\ = > (x - \frac{1}{x} ) = + 3 \: \: or \: \: - 3\end{gathered}x2+x21=11=>(x−x1)2+2=11=>(x−x1)2=11−2=9=>(x−x1)=+3or−3

2) Case : 1

When

x - \frac{1}{x} = 3x−x1=3

then,

\begin{gathered} {x}^{3} - \frac{1}{ {x}^{3} } = {(x - \frac{1}{x})}^{3} + 3(x - \frac{1}{x} ) \\ = > {3}^{3} + 3 \times 3 \\ = > 27 + 9 = 36\end{gathered}x3−x31=(x−x1)3+3(x−x1)=>33+3×3=>27+9=36

3) Case :2

When

x - \frac{1}{x} = - 3x−x1=−3

then,

\begin{gathered} {x}^{3} - \frac{1}{ {x}^{3} } = {( - 3)}^{3} + 3 \times ( - 3) \\ = > - 27 - 9 \\ = > - 36\end{gathered}x3−x31=(−3)3+3×(−3)=>−27−9=>−36

So,

x^3 - 1/x^3 = ±36

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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