SOLUTION: there are two real numbers. taking half of one is the same as adding 12.5 to the other; the square of the two real numbers are 200 apart
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-> SOLUTION: there are two real numbers. taking half of one is the same as adding 12.5 to the other; the square of the two real numbers are 200 apart
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You can put this solution on YOUR website! there are two real numbers.
a & b
taking half of one is the same as adding 12.5 to the other;
.5a = b + 12.5
multiply both side by 2
a = 2(b+12.5)
a = 2b + 25
the squares of the two real numbers are 200 apart
a^2 - b^2 = 200
replace a with (2b+25)
(2b+25)^2 - b^2 = 200
FOIL
4b^2 + 100b + 625 - b^2 = 200
4b^2 - b^2 + 100b + 625 - 200 = 0
3b^2 + 100b + 425 = 0
You can use the quadratic formula a=3; b=100 c=425, this will factor to:
(3b + 85)(b + 5) = 0
3b = -85
b = -85/3
b =28.3333
and
b = -5, let's stick with the integer
find a
a =2(-5) + 25
a = -10 + 25
a = +15
:
The 2 numbers are 15 and -5
:
:
Check in the equation a^2 - b^2 = 200
15^2 - (-5^2) =
225 - 25 = 200
