Question

If a=1/a-5 find a+1/a​

Answer 1

1-5= -4

a+1/a = 1+1/1 so, 1+1=1

1/1= 1 ans

Answer 2

Answer:

5

Step-by-step explanation:

Given that -

$\implies \sf a = \frac{1}{a} - 5 \\ \\ \implies \sf a - \frac{1}{a} = - 5 \\ \\ \bf squaring \: both \: sides - \\ \\ \implies \sf (a - \frac{1}{a} ) {}^{2} = ( - 5) {}^{2} \\ \\ \implies \sf a {}^{2} + \frac{1}{a {}^{2} } + 2 = 25 \\ \\ \implies \sf a {}^{2} + \frac{1}{a {}^{2} } = 25 - 2 \\ \\ \implies \sf a {}^{2} + \frac{1}{a {}^{2} } = 23$

Now, adding two both sides-

$\implies \sf a {}^{2} + \frac{1}{a {}^{2} } + 2 = 23 + 2 \\ \\ \implies \sf( a + \frac{1}{a}) {}^{2} = 25 \\ \\ \implies \sf( a + \frac{1}{a}) = \sqrt{25} \\ \\ \boxed{ \boxed{ \bf a + \frac{1}{a} = 5}}$

Hence, the answer is 5.

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• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)