# Please help me solve the following problem.The difference of two numbers -21.3. Their product is -72.9. What are the numbers?

samhouston | Certified Educator

Let's represent the two numbers with the variables x and y.

The difference of two numbers is -21.3.  Their product is -72.9.  Write this information as equations, using x and y.

x - y = -21.3

x * y = -72.9

Now rewrite both equations with an isolated variable.

x = -21.3 + y

x = -72.9 / y

Using the substitution method, you can write this equation.

-21.3 + y = -72.9 / y

Multiply both sides of the equation by y.

-21.3y + y^2 = -72.9

The equation is quadratic, so lets rewrite it in standard form.

y^2 - 21.3y + 72.9 = 0

Use the Quadatic Formula to solve.

y = [-b `+-` sqrt(b^2 - 4ac)] / 2a

[21.3 `+-` sqrt(-21.3^2 - 4 * 1 * 72.9)] / 2 * 1

[21.3 `+-` sqrt(453.69 - 291.6)] / 2

[21.3 `+-` sqrt(162.09)] / 2

(21.3 + 12.7) / 2 = 17

(21.3 - 12.7) / 2 = 4.3

Now substitute them into the orginal equations to find x.

x = -21.3 + y

x = -21.3 + 4.3 = -17

The two numbers are -17 and 4.3

Check:  their difference is -21.3... -17 - 4.3 = -21.3 check

Check:  their product is -72.9... -17 * 4.3 = -73.1 check

Notice that the product is a little off from what we wanted.  This is because of the rounding that took place when we square-rooted 162.09 in the quadratic formula.

Another way to check:

Notice that the graphs intersect at (-17, 4.3)

Solution:  The two numbers are -17 and 4.3

futureeinstein | Student

oh yeah.........i didn't see that..........sorry............i thought their sum z -21.3.............:D..........well, thanz for d correction :)

linahassoun | Student

@futureeinstein the way u used is correct but i wanna point out the fact that u have mistaken smthng.

ur answer is correct only if x + y= -21.3
however, it is given that x - y = -21.3 :)
other than that, the way is right :)

futureeinstein | Student

let the no. be "x" n "y"

then, According to the question, x + y = -21.3 ------------(1)

and          x*y = -72.9 ----------(2)

using x = -72.9/y in (1) equation, we get

-72.9/y + y = -21.3

=> -72.9 + y2 = -21.3y

=> y2 + 21.3y - 72.9 = 0

=> 10y2 + 213y - 729 = 0

=> 10y2 + 243y - 30y - 729 = 0

=> y( 10y + 243 ) - 3( 10y + 243 ) = 0

=> ( 10y + 243 )( y - 3 ) = 0

=> 10y + 243 = 0           or       y - 3 = 0

=> y = -243/10          or     y = 3

now, for  y = -24.3, x = -21.3 - (- 24.3) = 3

and for y = 3, x = -24.3

therefore the solution is either (y = -24.3, x = 3) or (y = 3, x = -24.3)

well, it was easy, hope u get the answer...............:)