Question

pls with process i will give 20 points

Answer 1

EXPLANATION.

⇒ (a - 1/a) = 9.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (a - 1/a)² = (9)².

As we know that,

Formula of :

⇒ (x - y)² = x² + y² - 2xy.

Using this formula in the equation, we get.

⇒ (a)² + (1/a)² - 2(a)(1/a) = 81.

⇒ a² + 1/a² - 2 = 81.

⇒ a² + 1/a² = 81 + 2.

⇒ a² + 1/a² = 83.

As we know that,

Formula of :

⇒ (x + y)² = (x - y)² + 4xy.

Using this formula in the equation, we get.

⇒ (a + 1/a)² = (a - 1/a)² + 4(a)(1/a).

⇒ (a + 1/a)² = (a)² + (1/a)² - 2(a)(1/a) + 4(a)(1/a).

⇒ (a + 1/a)² = a² + 1/a² - 2 + 4.

⇒ (a + 1/a)² = a² + 1/a² + 2.

Put the value of (a² + 1/a² = 83) in the equation, we get.

⇒ (a + 1/a)² = 83 + 2.

⇒ (a + 1/a)² = 85.

Answer 2

$\tt \underline\purple{Given:-}$

$\: \: \: \: \: \: \bullet\sf{ \: \: {a}^{2} + \frac{1} {a}^{2} = 83 }$

$\: \: \: \: \: \: \: \bullet\sf{ \:( a + \frac{1}{a}) ^{2} = 85}$

$\tt\underline\purple{Find:-}$

• The value of the question.

$\tt\underline\purple{Solution:-}$

$\begin{gathered}\begin{gathered}{\large \qquad \boxed{\boxed{\begin{array}{cc} \sf(i) \: \: \bf \: {a}^{2} + \frac{1}{ {a}^{2} } = 83 \\ \\ \ \sf \mapsto \: {a}^{2} + \frac{1}{ {a}^{2} } = \frac{2a}{1a} = 81 \\ \\ \sf \mapsto \: {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 81 \\ \\ \sf \mapsto \: {a}^{2} + \frac{1}{ {a}^{2} } = 81 + 2 \\ \\ \sf \dashrightarrow \purple{{a}^{2} + \frac{1}{ {a}^{2} } = 83} \\ \\ \\ \\ \bf (ii)(a + \frac{1}{a} ) ^{2} = 85 \\ \\ \sf \mapsto( \frac{a - 1}{a}) ^{2} + 4a \times 1a \\ \\ \sf \mapsto \: {a}^{2} + \frac{1}{ {a}^{2} } = 83 \\ \\ \sf \mapsto \: 83 + 2 \\ \\ \dashrightarrow \sf \fbox \purple{85} \end{array}}}}\end{gathered}\end{gathered}$

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Note :

• See this answer in brainly website link :https://brainly.in/question/47194038

@Shivam

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