Question

if x+1/x=6, find (i) x-1/x (ii) x2-1/x2​

Answer 1

Answer:

(1) 4root2 (2) 34

Step-by-step explanation:

(x--1/x)^2=(x+1/x)^2--4.x.1/x=32 so x--1/x=4 root 2 and x^2--1/x^2=34

Answer 2

$x + \frac{1}{x} = 6...(1) \\ ( {x + \frac{1}{x} })^{2} = 36 \\ ( {x - \frac{1}{x} })^{2} + 4 = 36 \\ ( {x - \frac{1}{x} })^{2} = 32 \\ x - \frac{1}{x} = 4 \sqrt{2} ...(2) \\ finding \: \: \: {x}^{2} - \frac{1}{ {x}^{2} } = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = 6 \times 4 \sqrt{2} \\ = 24 \sqrt{2}$