Question

if a-1/a =5, then find the value of a+1/a​

Answer 1

GIVEN :-

• a - 1/a = 5.

TO FIND :-

• The value of a + 1/a

SOLUTION :-

$\\ : \implies \displaystyle \sf \: a - \dfrac{1}{a} = 5$

$\bullet \: \displaystyle \sf Squaring \: Both \: Sides.$

$: \implies \displaystyle \sf \: \bigg( a - \dfrac{1}{a} \bigg) ^{2} = \bigg (5 \bigg ) ^{2}$

$\bullet \displaystyle \sf \: using \: identity \to (a - b)^{2} = a^{2} + b^{2} - 2ab$

$: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} - 2 \times a \times \frac{1}{a} = 25$

$: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} - 2 = 25$

$: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} = 25 + 2$

$: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} = 27$

$: \implies \underline{ \boxed{\displaystyle \sf \: a+ \frac{1}{a} = \pm \: \sqrt{27}}}$

$\therefore \underline {\displaystyle \sf Required \ answer \ is \ \pm \sqrt{27}}$

Answer 2

GIVEN :-

a - 1/a = 5.

TO FIND :-

The value of a + 1/a

SOLUTION :-

$\begin{gathered}\\ : \implies \displaystyle \sf \: a - \dfrac{1}{a} = 5 \\ \\ \\\end{gathered} </p><p>$

$\begin{gathered}\bullet \: \displaystyle \sf Squaring \: Both \: Sides. \\ \\ \\\end{gathered} </p><p></p><p>$

$\begin{gathered}: \implies \displaystyle \sf \: \bigg( a - \dfrac{1}{a} \bigg) ^{2} = \bigg (5 \bigg ) ^{2} \\ \\ \\\end{gathered}$

$\begin{gathered}\bullet \displaystyle \sf \: using \: identity \to (a - b)^{2} = a^{2} + b^{2} - 2ab\\ \\ \\\end{gathered} </p><p>∙$

$\begin{gathered}: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} - 2 \times a \times \frac{1}{a} = 25 \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} - 2 = 25 \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} = 25 + 2 \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \displaystyle \sf \: \bigg(a+ \frac{1}{a} \bigg) ^{2} = 27 \\ \\ \\\end{gathered}$

$\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \: a+ \frac{1}{a} = \pm \: \sqrt{27}}} \\ \\\end{gathered}$

$\therefore \underline {\displaystyle \sf Required \ answer \ is \ \pm \sqrt{27}}∴$