Question

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if a+1/a²=6,then a²+1/a²

Answer 1

Correct Question :-- if (a+1/a) = 6 , Find a² + 1/a² ?

Formula used :--

• (a+b)² = a² + b² + 2ab

Solution :--

→ (a+1/a) = 6

Squaring both sides we get,

→ (a+1/a)² = 6²

→ (a² + 1/a² + 2 * a * 1/a) = 36

→ a² + 1/a² + 2 = 36

→ a² + 1/a² = 36 -2

→ a² + 1/a² = 34 . (Ans).

Hence, The value of (a² + 1/a²) will be 34.

Answer 2

$\Huge{\underline{\green{\mathfrak{Ans}}{\mathfrak{wer :}}}}$

$\rule{200}{2}$

$\LARGE{\red{\bigstar}} {\underline{\orange{\sf{To \: Find :}}}}$

We have to find the value of,

$\sf{a^2 + \frac{1}{a^2}}$

$\rule{200}{2}$

$\LARGE{\red{\bigstar}} {\underline{\orange{\sf{Solution :}}}}$

$\sf{a + \frac{1}{a} = 6 .......(1)} \\ \\ \bf{Squaring \: both \: sides \: in \: equation \: 1.}$

Using Identity :

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$\Large{\sf{(a + b)^2 = a^2 + b^2 +2ab}}$

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We get,

$\sf{→a^2 + (\frac{1}{a})^2 + 2(\cancel a)(\frac{1}{\cancel a}) = 36}\\ \\ \sf{→a^2 + \frac{1}{a^2} + 2 = 36} \\ \\ \sf{→a^2 + \frac{1}{a^2} = 36 - 2}\\ \\ \sf{→a^2 + \frac{1}{a^2} = 34}$