Question

Q.19-If a+(1/a) =√2 then calculate the value of a^2+1/a^2
A) 0
B) 1
C) 2
D) 3
E) 4​

Answer 1

Answer:

this is your answer

$a + ( \frac{1}{a} ) = \sqrt{2} \\ {a}^{2} + { \frac{1}{a} }^{2} \\ \\ { { \sqrt{2} }^{2} }^{2} \\ \\ {2}^{2} = 4$

Answer 2

In given Eq. → a + $\sf \frac{1}{a} = \sqrt{2}$ Take square from both sides

→ $\sf \bigg( a +\frac{1}{a} \bigg)^2 = (\sqrt{2})^2$

Here we can apply Identity of (a + b)² = a² + b² + 2ab

Hence,

→ $\sf (a)^2 + \bigg( \frac{1}{a} \bigg) ^2 + 2(a)\bigg(\frac{1}{a} \bigg) = (\sqrt{2})^2$

→ $\sf a^2 + \frac{1}{a^2} + 2(\cancel{a)}\bigg(\frac{1}{\cancel{a}} \bigg) = 2$

→ $\sf a^2 + \frac{1}{a^2} + 2 = 2$

→ $\sf a^2 + \frac{1}{a^2} = 2 - 2$

→ $\sf a^2 + \frac{1}{a^2} = 0$

Hence, Answer is (A) 0

I hope it helps you ❤️✔️