What 2 numbers add up to -57 and multiply to -1540?

Question

this math question.. i've been trying to figure out for like forever... lol (actually like 5 min. but whatever)

Answer 1

suppose that the numbers = x&y

then
xy = -1540
x = -1540/y

x + y = -57
-1540/y + y = -57...............*y
-1540 + y² = -57y
y² + 57y -1540 = 0
(y - 20 ) (y +77) = 0
y - 20 = 0
y = 20 ..
then x = 1540/20 = -77
OR
y + 77 = 0
y= -77...
then x = 1540/-77 = 20

So the numbers are 20 , -77

Answer 2

let x=the first number
let y=the second number

x+y=-57
x=-57-y now hold onto that

x*y=-1540
substitute x for what you solved it to be in the first equation
(-57-y)*y=-1540
y^2+57=1540
y^2+57-1540=0
(y-20)(y+77)=0
y=20, -77

now insert that into the original equation to see which value works

y=20: x=-57-20=-77 ----> -57*20=-1540 it works
y=-77: x=-57+77= -20 ----> -20*-77=1540 doens't work


so the numbers are 20 and and -77

Answer 3

If AxB=-1540, then if A is positive, B is negative.

Guess A = - 100, so B = 43
AB = - 4300
this is too high, so try A = - 90, B = 33
AB = - 2970
still too high, so try A = - 80, B = 23
AB = -1840
closer, so try A = -70, B = 13
AB = - 910
too low.
so your answer is between -80 and -70 for A
and between 23 and 13 for B. Use "guess and
check" until you find the right pair. If you have to
show your work, make a chart showing
....A | B..|..AB
-100|.33.|-4300
..-90|.23.|-2970
..-80|.13.|-1840
etc.
until you have the right answer that gives -1540

Answer 4

I'm assuming the answer is in whole numbers.

Find all the factors of -1540 and see which ones add up to -57.

Or you could solve the following equation: y2 -57y+1540=0

That would give you the value of y.

Answer 5

x + y = -57
xy = -1540

y = -x - 57

(-x - 57)x = -1540
-(x + 57)x = -1540
(x + 57)x = 1540
x^2 + 57x = 1540
x^2 + 57x - 1540 = 0

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-57 ± sqrt(57^2 - 4(1)(-1540)))/(2(1))
x = (-57 ± sqrt(3249 + 6160))/2
x = (-57 ± sqrt(9409))/2
x = (-57 ± 97)/2
x = (40/2) or (-154/2)
x = 20 or -77

ANS : 20 and -77

Answer 6

x + y = -57
xy = -1540

y = -57 - x
x(-57 - x) = -1540
-57x -x^2 = -1540
x^2 + 57x + 1540 = 0

find x, plug into 1st equation, find y

Answer 7

-77 and 20

Answer 8

-77 and 20

Answer 9

x+y=-57
x=-57-y
xy=-1540
(-57-y)y=-1540
-57y-y^2=-1540
y^2+57y-1540=0
y=(-57+/-√(57^2+4*1540))/2
y=(-57+/-√(3249+6160))/2
y=(-57+/-√(9409))/2
y=(-57+/-97)/2
y=(-57-97)/2=-77
y=(-57+97)/2=20

the numbers are -77 & 20