Question

$\huge\tt\red{P}\tt\pink{L}\tt\blue{E}\tt\green{A}\tt\purple{S}\tt\orange{E}$ $\huge\tt\red{A}\tt\pink{N}\tt\blue{S}\tt\green{W}\tt\purple{E}\tt\orange{R}$ ■correct answer will be marked as brainlist■ ■ wrong answer will be reported ​■​

Answer 1

Answer:

$\sqrt{ {a}^{2} + (1 \div {a}^{2} ) \: - 2} = a \: - (1 \div a) \\ a \: - (1 \div a) = \sqrt{786 - 2} \\ a - (1 \div a) = \sqrt{784} = 28 \\ hence \: answer \: is \: \: 28$

Answer 2

★ Given:

${\mapsto} \: {\sf{ {a}^{2} + \frac{1}{ {a}^{2} } = 786 }}$

★ To find:

${\mapsto} \: {\sf{a - \frac{1}{a} }}$

★ Solution:

${\mapsto}{\sf{ ({a - \frac{1}{a}) }^{2} = {a}^{2} - 2 \times{\cancel a }\times \frac{1}{\cancel{a}} + {\frac{1}{ {a}^{2} }}}}$

${\mapsto}{\sf{ ({a - \frac{1}{a}) }^{2} = {a}^{2} + {\frac{1}{ {a}^{2} } - 2}}}$

${\mapsto} \: {\sf{ ({a - \frac{1}{a} )}^{2} = 786 - 2}}$

${\mapsto} \: {\sf{ ({a - \frac{1}{a} )}^{2} = 784}}$

${\mapsto} \: {\sf{ a - \frac{1}{a} = \sqrt{784} }}$

${\mapsto} \: {\sf{ a - \frac{1}{a} = ± 28}}$

✠ Formula used:

${\boxed{\sf{\red{\bold{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }}}}}$