Question 97248Given equation {{{ 2x^(2/3) - 5x^(1/3) - 3 =0 }}} {{{ 2(x^(1/3))^2 - 5x^(1/3) - 3 =0 }}} Let {{{ x^(1/3) = A }}} the equation above transforms to {{{ 2A^2 - 5A -3 =0 }}} Using the midterm factorisation we rewrite the expression as {{{ 2A^2 - 6A + A -3 =0 }}} {{{ 2A(A-3) +1(A-3) =0 }}} {{{(A-3)(2A+1)=0}}} therefore {{{A-3=0}}} or {{{A=3}}} and {{{2A +1 =0}}} or {{{A =-1/2}}} Substituting A back as {{{ x^(1/3)}}} {{{ x^(1/3)}}} = 3 Cubing both sides {{{ x = 3^3 }}} {{{x=27}}} is one solution Again for A= -1/2 we have {{{ x^(1/3) = -1/2}}} Cubing both sides {{{ x = -1/8}}} Hence x = { -1/8,27} You can substitute these values of x in the original equation to verify the answers.