Question

Q5. If 2(x^2+1)=5x , find :
(1) x-1/x
(2) x^3-1/x^3​

Answer 1

Answer:

$2 {x}^{2} + 2 = 5x \\ 2x^{2} - 5x + 2 = 0\\ factorisation \: (4 \times 1 \: is \: 4 \: and \: addition \: of \: digits \: is \: 5) \\ 2 {x}^{2} - 4x - x + 2 \\ 2x(x - 2) - 1(x - 2) \\ (x - 2) \: (2x - 1) \\ hence \\ x = 2 \: and \\ 2x = 1 \\ x = \frac{1}{2} \\ now \\ (1) \: x - \frac{1}{x} \: \: \: (put \: x = 2) \\ 2 - \frac{1}{2} = \frac{3}{2} \\ and \\ (2) \: \frac{ {x}^{3} - 1}{ {x}^{3} } = \frac{ {2}^{3} - 1}{ {2}^{3} } = \frac{8 - 1}{8} = \frac{7}{8}$