Question

A=3-2√2,find a²+1/a²

Answer 1

heye dear here is your answer

A=3-2√2
formulae = a²+1/a²
put the value of A in equation

=) a²+1/a² =
=) (3-2√2)² + 1/(3-2√2) =) 9-2(3-2√2)+(2√2)²+1/(3)²-2(3-2√2)+(2√2)²
=) 9-6-4√2+4(2)+1/ 9-6-4√2+4(2)
=) 3-4√2 +8+1/3-4√2+8
=) 3+8+1-4√2= 3+8-4√2
=) 12-4√2=11-4√2
=) 12-11=4√2-4√2
=) 1 =0
then answer is 1
please mark as brain list answer please

Answer 2

Heya there !!!
Here is the answer you were looking for :

Identities used :

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ (x + y)(x - y) = {x}^{2} - {y}^{2}$

$a = 3 - 2 \sqrt{2} \\ \\ \frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} }$

On rationalizing the denominator we get,

$\frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \\ \frac{1}{a} = \frac{3 + 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2} )}^{2} } \\ \\ \frac{1}{a} = \frac{ 3 + 2 \sqrt{2} }{9 - 8} \\ \\ \frac{1}{a} = 3 + 2 \sqrt{2} \\ \\ a + \frac{1}{a} = (3 - 2 \sqrt{2} ) + (3 + 2 \sqrt{2} ) \\ \\ a + \frac{1}{a} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} \\ \\ a + \frac{1}{a} = 6$

On squaring both the sides we get,


${(a + \frac{1}{a} )}^{2} = {(6)}^{2} \\ \\ {(a)}^{2} + {( \frac{1}{a} )}^{2} + 2 \times a \times \frac{1}{a} = 36 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 36 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } = 36 - 2 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } = 34$

Hope this helps!!!

If you have any doubt regarding to my answer, feel free to ask in the comment section ^_^

@Mahak24

Thanks...
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