2X2311X13400 Key 512 1258 Please explain thank youSolution2x

2X^2/3-11X^1/3-40=0

Key: 512, -125/8

Please explain thank you

Solution

2x^2/3 -11x^1/3 - 40=0 . Let x^1/3 = y. Then the given equation changes to 2y² -11y - 40 = 0. On using the quadratic formula, we get y = [ 11± { (-11)² -4*2*(-40)}]/2*2 = [11± (121+320)]/4 = (11± 441)4 = (11± 21)/4 . Thus x^1/3 = y = (11+21)/4 = 32/4 =8 or, y = (11-21)/4 = -10/4 = -5/2. Hence x = 8³ = 512 or, x = (-5/2)³ = -125/8.