Question

8x^(3)-27=0

find the roots of x

Answer 1

`\sf Root \: of \: x \: are \: (3)/(2) \: and \: ( - 6 \pm √( - 108) )/(8)`

Explanation:

`\rm \implies 8 {x}^(3) - 27 = 0 \\ \\ \rm \implies (2 * 2 * 2) {x}^(3) - (3 * 3 * 3) = 0 \\ \\ \rm \implies {(2x)}^(3) - {3}^(3) = 0 \\ \\ \boxed{ \rm {a}^(3) - {b}^(3) = (a - b)( {a}^(2) + ab + {b}^(2) )} \\ \\ \rm \implies (2x - 3)( {(2x)}^(2) + (2x)(3) + {3}^(2) ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^(2) + 6x + 9 = 0 \\ \\ \rm \implies x = (3)/(2) \: and \: x = ( - 6 \pm √(36 - 144) )/(8) \\ \\ \rm \implies x = (3)/(2) \: and \: x = ( - 6 \pm √( - 108) )/(8)`