Question

X+1/x =3 then x²+1/x² is equal to​

Answer 1

Answer: 7

Step-by-step explanation:

$\red{ \underline{ \mathcal{GIVEN:}}} \: \blue{ x + \frac{1}{x} = 3. } \\ \red{To \: find \: the \: value \: of \: \blue{ {x}^{2} + \frac{1}{ {x}^{2} }} .} \\ \green {So, \: squaring \: both \: the \: sides \: of \: given \: equation.} \\ \blue{ \implies {(x + \frac{1}{x} )}^{2} = {3}^{2}. } \\ \green{ \boxed{Using: \: {(a + b)}^{2} = ({a}^{2} + {b}^{2} + 2ab) }} \\ \blue{ \therefore{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 x \times \frac{1}{x} = 9.}} \\ \green{After \: cancellation \: it \: will \: become:} \\ \blue{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9 } \\ \green{Subtract \: 2 \: on \: both \: the \: sides.Then,} \\ \blue{ \underline{{x}^{2} + \frac{1}{ {x}^{2} } = 7.}}$

Answer 2

Step-by-step explanation:

⠀⠀⠀⠀⠀⠀⠀$\pmb\: x + \cfrac{1}{x} = 3 \: \\ \\ {\bigg(\pmb \: x + \cfrac{1}{x} \bigg) }^{2} = {3}^{2} \\ \\\pmb \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 9 \\ \\\pmb \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 9 - 2 \\ \\ \boxed{\pmb \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 7}$