Question

Express `24/(18 - x) - 24/(18 + x) = 1` as a quadratic equation in standard form and find the discriminant of the quadratic equation, so obtained. Also, find the roots of the equation.

Answer 1

Given equation is

`24/(18 - x) - 24/(18 + x) = 1`

⇒ `(24(18 + x) - 24(18 - x))/((18 - x)(18 + x)) = 1`

⇒ `(24{(18 + x) - (18 - x)})/(18^2 - x^2) = 1`

⇒ `(24(2x))/(324 - x^2) = 1`

⇒ 48x = 324 – x²

⇒ x² + 48x – 324 = 0

Here a = 1, b = 48, c = –324

Discriminant (D) = b² – 4ac

= 48² – 4(1)(–324)

= 2304 + 1296

= 3600

Roots are `(-b ± sqrt(D))/(2a)`

∴ Root = `(-48 ± sqrt(3600))/(2 xx 1)`

= `(-48 ± 60)/2, (-48 - 60)/2`

= 6, –54