Question

If (y + 1/y) = 8
then, (y² +1/y²) is?

Give full explanation!​

Answer 1

$\purple{\bf{\underline {Solution:-}}}$

${\tt{y+\frac{1}{y} = 8}}$

$\tt{⟹ {(y + \frac{1}{y}) }^{2} } = {8}^{2}$

$\tt{⟹ {y}^{2} + 2 \times y \times \frac{1}{y} + \frac{1}{ {y}^{2} } = 64}$

$\tt{⟹ {y}^{2} + 2 + \frac{1}{ {y}^{2} } = 64 }$

$\tt{⟹ {y}^{2} + \frac{1}{ {y}^{2} } = 64 - 2 }$

$\tt{⟹ {y}^{2} + \frac{1}{ {y}^{2} } = 62 }$

____________________________

$\blue {\bf {\underline{Some~Important\:Formulas:}}}$

• ${(a+b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

• ${(a-b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

• ${(a+b)}^{2} = {(a-b)}^{2} + 4ab$

• ${(a-b)}^{2} = {(a+b)}^{2} - 4ab$

• ${a}^{2} - {b}^{2} = (a+b)(a-b)$

• ${a}^{2} + {b}^{2} = {(a+b)}^{2} - 2ab$

• ${a}^{2} + {b}^{2} = {(a-b)}^{2} + 2ab$

• $4ab = {(a+b)}^{2} - {(a-b)}^{2}$

• $2 ({a}^{2}+{b}^{2}) = {(a+b)}^{2} + {(a-b)}^{2}$

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

please mark the answer as brainliest and thank the answer.