Question

X^2+1/x^2 =26 Find a)x+1/x b)x-1/x

Answer 1

Answer:

6 and -4

Step-by-step explanation:

$\frac{{x}^{2} + 1}{ {x}^{2} } = 26 \\ {x}^{2} + 1 = 26 {x}^{2} \\ 25 {x}^{2} \: \: \: \:= 1 \\ x \: \: \: \: \: \: \: \: \: \: \:= \sqrt{ \frac{1}{25} } \\ x \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{5}$

$a) = \frac{x + 1}{x} \\ = \frac{ \frac{1}{5} + 1}{ \frac{1}{5} } \\ = \frac{ \frac{6}{5} }{ \frac{1}{5} } \\ = 6 \\ b) \frac{x - 1}{x} \\ = \frac{ \frac{1}{5} - 1}{ \frac{1}{5} } \\ = \frac{ \frac{ - 4}{5} }{ \frac{1}{5} } \\ = - 4$