Question

If f(x) =x +(1/x)=4, then find x² + (1/x ²)

Answer 1

x + 1/x = 4

Square both sides

x² + 1/x² + 2x(1/x) = 4²

(Using (a + b)² = a² + b² + 2ab)

→ x² + 1/x² + 2 = 16

→ x² + 1/x² = 14

Hence the answer is 14.

Answer 2

$\sf \red \bigstar \: GIVEN$

➝ f (x) = x +(1/x) = 4,

$\sf \pink \bigstar \: SQUARE \: BOTH \: SIDES$

$\sf \: ➝ \: {x}^{2} + \dfrac{1}{x} ^{2} + 2x \: ( \dfrac{1}{x}) = {4}^{2}$

$\sf \green \bigstar \: USING \: PROPERTY \: = (a + b) ^{2}$

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

$\sf \: = (x ^{2} ) + ( \dfrac{1}{x}^{2}) + 2 = 16$

$\sf \red{\: = x ^{2} + ( \dfrac{1}{x} ^{2} ) = 14}$

${ \sf {\green {hence \: the \: answer \: is \: 14.}}}$

$\huge {\pink{\frak{@misscuteangel}}}$