Question

if a+1/a =3 find a²+1/a²

Answer 1

hiii,

a + 1/a = 3
=>(a + 1/a)^ = 3^2
=>a^2 + 2. a. 1/a + 1/a^2 = 9
=>a^2 + 2 + 1/a^2 = 9
=> a^2 + 1/a^2 = 9-2 = 7

hope helps

Answer 2

Answer:

$a^{2}+\frac{1}{a^{2}}= 7$

Step-by-step explanation:

$Given \: a + \frac{1}{a}=3$

On Squaring both sides of the equation, we get

$\left(a+\frac{1}{a}\right)^{2}=3^{2}$

/* By an algebraic identity:

(x+y)² = x²+y²+2xy */

$\implies a^{2}+\frac{1}{a^{2}}+2\times a \times \frac{1}{a}= 9$

$\implies a^{2}+\frac{1}{a^{2}}+2= 9$

$\implies a^{2}+\frac{1}{a^{2}}= 9 -2$

$\implies a^{2}+\frac{1}{a^{2}}= 7$

Therefore,

$a^{2}+\frac{1}{a^{2}}= 7$

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