SOLUTION: what two numbers add to -3/2 and multiply to -1

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Question 698830: what two numbers add to -3/2 and multiply to -1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let's numbers be x and y
if two numbers add to -3%2F2, we have
x%2By=-3%2F2....eq. 1
and if they multiply to -1, we have
xy=-1...eq. 2
solve the system:
x%2By=-3%2F2....eq. 1
xy=-1...eq. 2
________________________
xy=-1...eq. 2....solve for x
x=-1%2Fy....substitute in eq. 1

-1%2Fy%2By=-3%2F2....eq. 1...solve for y

-1%2Fy%2By%2Ay%2Fy=-3%2F2
%28-1%2By%2Ay%29%2Fy=-3%2F2
%28-1%2By%5E2%29%2Fy=-3%2F2...cross multiply
%28-1%2By%5E2%29%2A2=-3%2Ay
-2%2B2y%5E2=-3y
2y%5E2%2B3y-2=0...use quadratic formula
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-2%29+%29%29%2F%282%2A2%29+
y+=+%28-3+%2B-+sqrt%28+9%2B16+%29%29%2F4+
y+=+%28-3+%2B-+sqrt%28+25+%29%29%2F4+
y+=+%28-3+%2B-+5+%29%2F4+
solutions:
y+=+%28-3+%2B+5+%29%2F4+
y+=+2%2F4+
y+=+1%2F2+
or
y+=+%28-3+-+5+%29%2F4+
y+=+-8%2F4+
y+=+-2+

now find x
x=-1%2Fy....plug in y+=+1%2F2+
x=-1%2F%281%2F2%29
x=-%281%2A2%29%2F1
x=-2
and
x=-1%2Fy....plug in y+=+-2+
x=-1%2F%28-2%29
x=1%2F2

so, the numbers are:
x=-2 and y+=+1%2F2+
or
x=1%2F2 and y+=+-2+