SOLUTION: If the sum of two numbers is 4 and the sum of their squares minus three times their product is 76 find the numbers

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Question 1206795: If the sum of two numbers is 4 and the sum of their squares minus three times their product is 76 find the numbers
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x and y
system%28x%2By=4%2Cx%5E2%2By%5E2-3xy=76%29

y=4-x
substituting,
x%5E2%2B%284-x%29%5E2-3x%284-x%29=76
x%5E2%2B16-8x%2Bx%5E2-12x%2B3x%5E2=76
5x%5E2-20x=60
divide both sides by 5,
x%5E2-4x=12
x%28x-4%29=12
Could the factors be 6 and 2?

6%286-4%29=12 yes.

Could the factors of 12 be -6 and -2?
-6%28-6-4%29
60, no.

x can be 6.
If that, then y=4-6
y=-2


The numbers, -2 and +6.

Check?
x=6;
6%5E2%2B%28-2%29%5E2-3%2A6%28-2%29
36%2B4%2B36
72%2B4
76


The numbers are -2 and +6.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The method for solving the problem shown by the other tutor is not good mathematics....

Let one number be x; then since the sum of the number is 4, the other number is 4-x.

The sum of the squares of the two numbers, minus three times their product, is 76:

x%5E2%2B%284-x%29%5E2-3x%284-x%29=76
x%5E2%2B16-8x%2Bx%5E2-12x%2B3x%5E2=76

5x%5E2-20x-60=0
x%5E2-4x-12=0
%28x-6%29%28x%2B2%29=0
x=6 or x=-2

If x=6, then 4-x=-2; if x=-2, then 4-x=6. Either way, the two numbers are -2 and 6.

ANSWER: -2 and 6