Question

if a=5+2√6 find a²+1/a²

Answer 1

$\huge \mathbb\green{ANSWER!!!!}$

Given -

• a = 5 + 2√6

To Find -

the value of

• a² + 1 / a²

Now, according to given information -

( 5 + 2√6)² + 1 / ( 5 + 2√6)²

here we use the formula of

(a + b)² = a² + b² + 2ab

• (5)² + (2√6)² + 2 × 5 × 2√6 + 1 / (5)² + (2√6)² + 2 × 5 × 2√6

• 25 + 24 + 20√6 + 1 / 25 + 24 + 20√6

• 50 + 20√6 / 49 + 20√6

Value of a² + 1 / a² is -

50 + 20√6 / 49 + 20√6 .

Answer 2

$hi \: friend....$

here's your answer ...

$a = 5 + 2 \sqrt{6}$

By squaring both sides.

${a}^{2} = ({5 + 2 \sqrt{6} )}^{2}$

${a}^{2} = 25 + 2(2 \sqrt{6})(5) + \\ ({2 \sqrt{6} })^{2}$

${a}^{2} = 25 + 20\sqrt{6} + 24$

${a}^{2} = 49 + 20 \sqrt{6}$

Therefore,

${a}^{2} + \frac{1}{ {a}^{2} } = \\ ( {49 + 20 \sqrt{6} )} + \frac{1}{49 + 20 \sqrt{6} }$

$= \frac{ ({49 + 2 0\sqrt{6} )}^{2} + 1}{49 + 2 0\sqrt{6} }$

$= \frac{9602 + 1}{98}$

$= \frac{9603}{98}$

$= 97.98$

$hope \: \: this \: \: helps....$