Question 40435
I assume that your expression is equated to zero, yes?
{{{x^2(2x-5)^2+x(5-2x)^3 = 0}}}
The term {{{(5-2x)^3}}} can be rewritten as: {{{-(2x-5)^3}}}, giving
{{{x^2(2x-5)^2-x(2x-5)^3 = 0}}}
Take out the common factor of {{{(2x-5)^2}}},
{{{(2x-5)^2(x^2 - x(2x-5)) = 0}}}
{{{(2x-5)^2(x^2 - 2x^2 + 5x) = 0}}}
{{{(2x-5)^2(5x - x^2) = 0}}}
{{{x(2x-5)^2(5 - x) = 0}}}
Since the product of the three terms, {{{x}}},{{{(2x-5)}}} and {{{(5-x)}}} is zero, then we equate each of the individual terms to zero as a solution to the problem. This gives us,
{{{x = 0}}}, {{{2x-5 = 0}}}, {{{5-x = 0}}}
Ans: {{{x = 0}}}, {{{x = 5/2}}}, {{{x = 5}}}
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Unfortunately, none of the solutions match your possible answers. I can't see anything wrong with my working. Is the expression supposed to be equated to zero ?