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 class="AM">`+-` sqrt(-21.3^2 - 4 * 1 * 72.9)] / 2 *
1
[21.3 `+-`
sqrt(453.69 - 291.6)] / 2
[21.3 class="AM">`+-` 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:
src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-30,1,-1,10,1,1,1,1,1,300,200,func,x+21.3,null,0,0,,,black,1,none,func,-72.9/x,null,0,0,,,black,1,none"/>
Notice
that the graphs intersect at (-17,
4.3)
Solution: The two numbers
are -17 and 4.3
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