+0

y= -340/X I need like table of the solutions

0
485
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the product of x and y equals -340 and the sum of x and y equals -3

Apr 3, 2015

#1
+94545
+10

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)

Apr 3, 2015

#1
+94545
+10

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)

CPhill Apr 3, 2015
#2
+95334
+5

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

Apr 3, 2015