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lys-0071 [83]
3 years ago
13

If x2 + y2 = 38 and x - y = 2, then what is x? If there are two possible answers, then enter the larger of the two.

Mathematics
2 answers:
Ket [755]3 years ago
7 0
If x-y=2 then x=2+y

And if you insert that in the first equation

(2 + y) {}^{2}  + y {}^{2}  = 38
4 + 4y + y {}^{2}  +  {y}^{2}  = 38
2y {}^{2}  + 4y - 34 = 0
y =  - 1 +  \sqrt{17}
Or
y =  - 1 -  \sqrt{17}


The first one is bigger so the answer is

y =  - 1 -  \sqrt{17}
sladkih [1.3K]3 years ago
4 0

Answer:

y= 3\sqrt{2} -1 \\x = 1 +3\sqrt{2}\\

Step-by-step explanation:

First we can find x from the linear equation. So:

If x-y=2 then x=2+y

After that. We can inster x value in the cuadratic equation:

(2 + y) {}^{2} + y {}^{2} = 38

4 + 4y + y {}^{2} + {y}^{2} = 38

2y {}^{2} + 4y + 4 - 38 = 0

2y {}^{2} + 4y -34 = 0

After reorganizing terms and using factorization methods:

2 (y+1)^2 - 36 = 0\\(y+1)^2 = 18\\y + 1 = +-\sqrt{18} \\y1 = 3\sqrt{2} -1 \\x1 = 2 -1 + 3\sqrt{2}=1 +3\sqrt{2}\\y2 = -1 - 3\sqrt{2}\\x2 = 2 -1 - 3\sqrt{2}=1 -3\sqrt{2}\\

Finally we choose the largest value for x.

y = 3\sqrt{2} -1 \\x = 1 +3\sqrt{2}\\

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