Question

solve it correctly
Do answer if u know otherwise ignore it​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

$\sf {a}^{2} + \frac{1}{ {a}^{2} } = 23$

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

$\sf \: a + \frac{1}{a}$

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \boxed { \bf \: ( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy} \\ \\ \therefore \: \bf \: {x}^{2} + {y}^{2} = ( {x + y)}^{2} - 2xy$

Here ,

• x = a

• b = 1/a

Putting values , we get...

$\\ \sf \: {a}^{2} + \frac{1}{ {a}^{2} } = ( {a + \frac{1}{a}) }^{2} - 2( \cancel{a})( \frac{1}{ \cancel{a}} ) \\ \\ \\ \sf \: 23 = ( {a + \frac{1}{a} )}^{2} - 2 \\ \\ \\ \sf \: ( {a + \frac{1}{a}) }^{2} = 25 \\ \\ \bf \: taking \: square \: root.. \\ \\ \sf \: a + \frac{1}{a} = \sqrt{25} \\ \\ \\ \underline{ \boxed{ \sf \: \blue{a + \frac{1}{a} = 5 }}}$

More identities :-

• ( x - y )² = x² + y² - 2xy

• ( x + y ) ( x - y ) = x² - y²

• ( x + a ) ( x + b ) = x² + ( a + b )x + ab

Answer 2

Answer:

cute DP...................<3