Question

If a=3+2√2 then find the value of a²+1/a²

Answer 1

Answer:

Step-by-step explanation:

a² = 9 + 8 + 12√2

1/a² = 1/(17+ 12√2)

Adding both,

17+12√2 + 1/(17+12√2)

= (17+12√2)² + 1/(1)

= 577+ 408√2

Pls mark as brainliest

Answer 2

a=3+2√2

Squaring on both sides,we get

a²=(3+2√2)²

a²=(3)²+(2√2)²+2(3)(2√2)

a²=9+8+12√2

a²=17+12√2 ...(i)

Now

$\frac{1}{ {a}^{2} } = \frac{1}{17 + 12 \sqrt{2} } \\ \frac{1}{ {a}^{2} } = \frac{1}{17 + 12 \sqrt{2} } \times \frac{17 - 12 \sqrt{2} }{17 - 12 \sqrt{2} } \\ \frac{1}{ {a}^{2} } = \frac{17 - 12 \sqrt{2} }{(17) ^{2} - (12 \sqrt{2}) ^{2} } \\ \frac{1}{ {a}^{2} } = \frac{17 - 12 \sqrt{2} }{289 - 288} \\ \frac{1}{ {a}^{2} } = \frac{17 - 12 \sqrt{2} }{1} \\ \frac{1}{ {a}^{2} } = 17 - 12 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: ...(ii)$

Adding (i) and (ii), we get

a²+1/a²=17+12√2+17-12√2

a²+1/a²=34