Question

If x+1/ 27, ind the values of each of the following:
1.
$x + \frac{1}{x}$
2.
$x - \frac{1}{x}$



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Answer 1

Given

• x²+1/x²= 27

To Find

• x+1/x
• x-1/x

Solution

_____________________

x+1/x

${~~~~\implies \sf \bigg ( x+\dfrac{1}{x}\bigg)^² = x² + \dfrac{1}{x²} + 2 × x × \dfrac{1}{x} }$

${~~~~\implies \sf \bigg ( x+\dfrac{1}{x}\bigg)^² = 27+ 2}$

${~~~~\implies \sf x+\dfrac{1}{x}=±\sqrt{29} }$

_____________________

x-1/x

${~~~~\implies \sf \bigg ( x-\dfrac{1}{x}\bigg)^² = x² + \dfrac{1}{x²} - 2 × x × \dfrac{1}{x} }$

${~~~~\implies \sf \bigg ( x+\dfrac{1}{x}\bigg)^² = 27-2}$

${~~~~\implies \sf \bigg ( x+\dfrac{1}{x}\bigg)^² = 25}$

${~~~~\implies \sf x+\dfrac{1}{x} = \sqrt{25}}$

${~~~~\implies \sf x+\dfrac{1}{x}= ±5}$

More to know

• $\begin{gathered}\begin{gathered}\begin{gathered}\blue{\begin{gathered}\tiny\begin{gathered}\small{\small{\small{\small{\small{\small{\small{\small{\small{\small{\begin{gathered}\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\red{ \bigstar} \: \underline{\bf{\orange{More \: Useful \: Formula}}}\\ {\boxed{\begin{array}{cc}\dashrightarrow \sf(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab \\\\\dashrightarrow \sf(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab \\\\\dashrightarrow \sf(a + b)(a - b) = {a}^{2} - {b}^{2} \\\\\dashrightarrow \sf(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b) \\\\ \dashrightarrow\sf(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b) \\ \\\dashrightarrow\sf a ^{3} + {b}^{3} = (a + b)(a ^{2} + {b}^{2} - ab) \\\\\dashrightarrow \sf a ^{3} - {b}^{3} = (a - b)(a ^{2} + {b}^{2} + ab \\\\\dashrightarrow \sf{a²+b²=(a+b)²-2ab}\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}}}}}}}}}}\end{gathered}\end{gathered}}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

hey your answer is in above pics

so pls mark it as brainliest