Question

Solve the following equation by using quadratic formula and give your answer correct to 2 decimal places : `2x - (1)/x = 1`

Answer 1

`2x - (1)/x = 1`

⇒ 2x² - 1 = 7x
⇒ 2x² - 7x - 1 = 0   ....(i)
Comparing (i) with ax² + bx + c, we get,
a = 2, b = -7, c = -1

∵ x = `(-b ± sqrt(b^2 - 4ac))/(2a)`

⇒ x = `(-(-7) ± sqrt((-7)^2 - 4(2) xx (-1)))/(2 xx 2)`

⇒ `(7 ± sqrt(49 + 8))/(4)`

⇒ `(7 ± sqrt(57))/(4)`

⇒ `x = (7 + sqrt(57))/(4) or x = (7 - sqrt(57))/(4)`

⇒ `x = (7 + 7.55)/(4) or x = (7 - 7.55)/(4)`

⇒ `x = (14.55)/(4) or x = (-0.55)/(4)`
⇒ x = 3.64 or x = -0.14.