If a= 3 + 2 √2 , then the value of a² + 1/ a² is *
Answers
Answer:
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\begin{gathered}a = 3 - 2 \sqrt{2} \\ \frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} } = \frac{3 + 2 \sqrt{2} }{(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} )} \\ \frac{1}{a} = \frac{3 + 2 \sqrt{2} }{9 - 8} = 3 + 2 \sqrt{2} \\ \\ now. \: a + \frac{1}{a} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} = 6 \\ \\ a - \frac{1}{a} = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} = - 4 \sqrt{2} \\ \\ thus \: \: \: {a}^{2} - \frac{1}{ {a}^{2} } = (a + \frac{1}{a} )(a - \frac{1}{a} ) \\ = 6 \times ( - 4 \sqrt{2}) = - 24 \sqrt{2}\end{gathered}
a=3−2
2
a
1
=
3−2
2
1
=
(3+2
2
)(3−2
2
)
3+2
2
a
1
=
9−8
3+2
2
=3+2
2
now.a+
a
1
=3−2
2
+3+2
2
=6
a−
a
1
=3−2
2
−3−2
2
=−4
2
thusa
2
−
a
2
1
=(a+
a
1
)(a−
a
1
)
=6×(−4
2
)=−24
2
Answer is 34
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