Question

If x+ 1/x = √5 then the value of x2 +1/x2 is (a) 3 (b) 2 (c) 5 (d) none of these

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\large{ \bold{ \red{ \underline{ \underline{Question...}}}}}$

$\large{ \sf{x + \frac{1}{x} = \sqrt{5} }} \: \large{ \sf{ find \: the \: {x}^{2} + \frac{ {1} }{ {x}^{2} } = ?}}$

$\large{ \green{ \bold{ \underline{ \underline{Answer...}}}}}$

$\large{ \sf{option \: (c )\: 3}}$

$\large{ \bold{ \red{ \underline{ \underline{Solution..}}}}}$

$\large{ \sf{ \to \: u \: must \: know}} \\ \\ \boxed{ \green{ \large{ \sf{(a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} }}}}$

$\large{ \sf{ \red{given} \: x + \frac{1}{x} = \sqrt{5} }} \\ \\ \large{ \sf{ \to \: (x + \frac{1}{x} ) {}^{2} = 5}} \\ \\ \large{ \sf{ \to {x}^{2} + 2 \times x \times \frac{1}{x} + ( \frac{1}{x} ) {}^{2} = 5}} \\ \\ \large{ \sf{ \to \: {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 5}} \\ \\ \large{ \sf{ \to {x}^{2} + \frac{1}{ {x}^{2} } = 5 - 2}} \\ \\ \large{ \sf{ \boxed{ \green{ \to \: {x}^{2} + \frac{1}{ {x}^{2} } = 3}}}}$

$\bold{ \large{ \orange{ required \: answer = 3}}}$