Question

if a+1/a=3 then a^2+1/a^2=?

Answer 1

$\sf a + \frac{1}{a} = 3$

Squaring both sides, we get,

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

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

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

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

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

Hence, the value of a²+1/a² is 7.

Answer 2

$\huge\mathbb\pink{\underline{\underline{Answer}}}$

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

To find $\longrightarrow$

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

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

Squaring both the sides.

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

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

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

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

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