Question

10) If a 1/a-3 then the value of a² + 1/a² a) 11 b) 13 c) 15 d) none​

Answer 1

EXPLANATION.

⇒ (a - 1/a) = 3.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (a - 1/a)² = (3)².

⇒ (a)² + (1/a)² - 2(a)(1/a) = 9.

⇒ a² + 1/a² - 2 = 9.

⇒ a² + 1/a² = 9 + 2.

⇒ a² + 1/a² = 11.

Option [A] is correct answer.

Answer 2

${ \boxed{\boxed{\begin{array}{cc} \bf \: given \\  \\ \rm \to \:a -  \frac{1}{a} = 3 \\  \\   \rm \: we \: have \: to \: find \\  \\ \rm \to \: the \: value \: of \:   \:  \:  \:  \: {a}^{2}  +  \frac{1}{ {a}^{2} }   \\  \\  \bf \: we \: know \: that \\  \\  \rm {a}^{2} +  \frac{1}{ {a}^{2} }  =   {(a -  \frac{1}{a} })^{2} + 2 \times a \times  \frac{1}{a}  \\  \\  =  {3}^{2}  + 2 \\  \\  = 9 + 2 \\  \\  = 11  \\  \\  =  \rm \: option \: (a)\end{array}}}}$