If a - 1-a - 3 find a-2 - 1-a-2- - Maths Q-A

Solve using the algebraic identities.We are given an equation as a + 1/a = 3On squaring both sides. we get⇒(a +1/a)^2 = 3^20ex0ex⇒a^2 + 2 + 1/a^2= 9 0ex0ex⇒a^ ...

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Standard XII

Mathematics

Global Maxima

If a + 1/a = ...

Question

If $a + \frac{1}{a} = 3$ find $a^{2} + \frac{1}{a^{2}}$

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Solution

Solve using the algebraic identities.
We are given an equation as
$a + \frac{1}{a} = 3$
On squaring both sides. we get
$\Rightarrow {(a + \frac{1}{a})}^{2} = 3^{2} \Rightarrow a^{2} + 2 + \frac{1}{a^{2}} = 9 \Rightarrow a^{2} + \frac{1}{a^{2}} = 9 - 2 \Rightarrow a^{2} + \frac{1}{a^{2}} = 7$
Hence, the required value of $a^{2} + \frac{1}{a^{2}}$ is $7$

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If a+1a=3 find a2+1a2

Solve using the algebraic identities.We are given an equation as a+1a=3On squaring both sides. we get⇒(a+1a)2=32⇒a2+2+1a2=9⇒a2+1a2=9-2⇒a2+1a2=7Hence, the required value of a2+1a2is 7

If $a + \frac{1}{a} = 3$ find $a^{2} + \frac{1}{a^{2}}$