Question

$x + 1 \div x = 5 \: find \: x {}^{2} + 1 \div x {}^{2}$
​

Answer 1

given :- x + 1/x = 5

➡ x + 1 = 5x

➡ x - 5x = -1

➡ -4x = -1

➡ x = -1/-4

➡ x = 1/4

therefore x² = (1/4)² = 1/16

and 1/x² = 1/1 × 16/1

= 16

hence, value of x² + 1/x²

= 1/16 + 16

LCM of 1 and 16 = 1 × 16

= 16

= 1/16 + 256/16

= 257/16 FINAL ANSWER

Answer 2

$\huge \boxed{ \bold \: {Solution}}$

$\implies \: x + 1 \div x = 5 \\ \\ \implies \: x + 1 \times \frac{1}{x} = 5$

$\\ \implies \: x + 1 = 5 \times x \\ \\ \implies \: x + 1 = 5x \\ \\ \implies \: x - 5x = - 1$

$\\ \implies \: - 4x \: = - 1 \\ \\ \implies \: x = \dfrac{ \cancel - 1}{{ \cancel- }4}$

$\large \boxed{ \bold{\implies \: x = \frac{1}{4} }}$

Now

$to \: find \: : x {}^{2} + 1 \div x {}^{2}$

Put the value of x

$\implies \: ( { \frac{1}{4} )}^{2} + 1 \div( \frac{1}{4} )^{2}$

$\implies \: \frac{1}{16} + 1 \times 16$

$\frac{1}{16} + 16$

$\large{\frac{1 + 256}{16} }$

$\large \boxed { \bold{ \underline{ \underline{\implies \: \frac{257}{ \: \: \: \: \: \: \: \: \: \: \: \: 16 \: \: \: \: \: \: \: \: \: \: \: \: \: \: } }}}}$