+128475 The product of x and y equals -340 and the sum of x and y equals -3
So we have
xy = -340 and
x + y = -3
We can transform the second equation to
y = -3 - x
And putting this into the first equation, we have
x(-3 -x) = -340 simplify
-3x - x^2 = -340 multiply through by -1
x^2 + 3x = 340 subtract 340 from each side
x^2 + 3x - 340 = 0 facror, if possible
(x +20)(x - 17) = 0 set each factor to 0
So
x = -20 and x = 17
And using y = -3 - x
When x = -20, y = -3- (-20) = 17
When x = 17 y = -3 - 17 = -20
So the solutions are (-20, 17) and (17, -20)
+128475 The product of x and y equals -340 and the sum of x and y equals -3
So we have
xy = -340 and
x + y = -3
We can transform the second equation to
y = -3 - x
And putting this into the first equation, we have
x(-3 -x) = -340 simplify
-3x - x^2 = -340 multiply through by -1
x^2 + 3x = 340 subtract 340 from each side
x^2 + 3x - 340 = 0 facror, if possible
(x +20)(x - 17) = 0 set each factor to 0
So
x = -20 and x = 17
And using y = -3 - x
When x = -20, y = -3- (-20) = 17
When x = 17 y = -3 - 17 = -20
So the solutions are (-20, 17) and (17, -20)
+118609 Thanks Chris, I am going to show how to do it another way.
your way always works (so long as there really is a solution) , mine only works for whole numbers.
the product of x and y equals -340 and the sum of x and y equals -3
If I am trying to factoize a quadratic and I am expecting integer answers (whole numbers)
I often use a 'guess' method.
1) They multiply to a neg number so one is positive and one is negative.
2) They add to a negative so the 'bigger' one is negative.
3) now I more or less forget about the negative signs for a bit.
4) they add to -3 so the numbers are close in value - only 3 apart.
5) Now I am going to look for factors of 340 that suit this.
340 = 34*10 = 2*17*2*5 = 2*2*5*17 = 20*17 that looks helpful, they are 3 apart
6) Must be -20 and +17
