Question 1208480
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What adds to -4 but multiplies to 24
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<pre>
They want you find x and y from these equations

    x + y = -4    (1)

      xy  = 24    (2)


From equation (1), express  x = -4 -y  and substitute it into equation (2).  You will get

    (-4-y)*y = 24,

    -4y - y^2 = 24

    y^2 + 4y + 24 = 0

    {{{x[1,2]}}} = {{{(-4 +- sqrt(4^2 - 4*24))/2}}} = {{{(-4 +- sqrt(16-96))/2}}} = {{{(-4 +- sqrt(-80))/2}}} = {{{(-4 +- 4i*sqrt(5))/2}}} = {{{-2 +- 2sqrt(5)*i}}}.


Thus, there are two possible answers:

    x = {{{-2 + 2*sqrt(5)*i}}},  y = {{{-2 - 2*sqrt(5)*i}}}

and

    x = {{{-2 - 2*sqrt(5)*i}}},  y = {{{-2 + 2*sqrt(5)*i}}}.


In both cases,  x + y = -2 - 2 = -4;  xy = {{{(-2)^2 - 2^2*(sqrt(5))^2*i^2}}} = 4 - 4*5*(-1) = 4 + 20 = 24.
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Solved.