2 numbers multiplied together equals 87 the same numbers added together equal 36?

xy = 87

x + y = 36

__________

Now solve for either x or y in the second equation:

x = 36 - y

Substitute this in for x in the first equation:

(36 - y)y = 87

36y - y² = 87

y² - 36y = -87

Complete the square:

y² - 36 + 324 = -87 + 324

(y - 18)² = 237

y - 18 = ±√237

y = 18 ± √237

Now solve for x:

x + (18 ± √237) = 36

x = 36 - 18 ± √237

x = 18 ± √237

It appears that x = y = 18 ± √237, however, it does not. Instead,

Let x = 18 + √237 ≈ 33.395

Let y = 18 - √237 ≈ 2.605

Plug these back in to the original equations and it should work out.

Select my answer as best answer. Thanks!!

There are no whole numbers that make this work. The only answer is that the two numbers are 18 + sqrt(237) and 18 - sqrt(237).

You get that answer by realizing that if the two numbers add up to 36 and one of them is x, the other must be 36 - x. Then the requirement that they multiply out to 87 gives you the equation

x(36 - x) = 87

36x - x^2 = 87

0 = x^2 - 36x + 87

Putting that into the quadratic formula, you get the answers I mentioned above:

18 + sqrt(237) and 18 - sqrt(237).

That might not be what you (or the teacher) are looking for, but they are the only answers that fit the problem. Believe me.

Maybe instead of 36 the numbers added together is 32 as follows: 2 numbers multiplied together equals 87 the same numbers added together equal 32? Then the solution will be:

x = 1st no., y = 2nd no.

Relative values of y:

xy = 87

y = 87/x

x + y = 32

y = 32 - x

Exact value of x:

x(32 - x) = 87

32x - x² = 87

x² - 32x + 87 = 0

(x - 3)(x - 29)

x = 3, 29

Answer: The two numbers are 3 and 29.

Proof:

3 + 29 = 32 as the sum of the two

3 * 29 = 87 as the product of the 2

But with the sum of 36 we go nowhere.

a + b = 36

ab = 87

its a system of equations. to solve, find what one number is in terms of the other number. So, using the equation a + b = 36, you can solve for either number, i'll choose b.

36 - a = b

then you substitue 36 - a for the b in the 2nd equation.

(36 - a)a = 87

then solve.

36a - a^2 = 87

0 = a^2 -36a +87

i guess you have to use the quadratic formula because there is no 2 numbers that multiply to equal 87 and add to equal 36.

[36 +/- sq. root (1296- 4 x 87)]/2

36 +/- sq. root (948)

[36 +/- 2 times sq root (237)]/2

18 + sq. root (237) and 18 - sq. root (237) are the only answers.

this means that the two numbers are 18 - sq. root (237) which is 2.605 and 18 + sq. root (237) which is 33.395. those add to equal 36 and multiply to equal 87.

6

let the two numbers be x and y then

xy=87

x+y=36

x=36 -y

Substitute in the first equation

(36-y)*y = 87

36y - y^2 =87

y^2 -36y +87 = 0

Solve the Quadratic formula to find y. IThere will be two values. one will satisfy the result. Then substitute the value in first eq to find x

x+y=36....x=36-y

Use substitution method to get equation in terms of y

x*y=87...(36-y)*y=87 solve for y. then plug back in to solve for x

thats impossible for me to figure out, but there was one that was how is 7 half of 12 and the answer was it was roman numeral 12 split in half.