((√50-√2))^2*(√2)^2= (50-2)*2=48*2=96 но лучше подожди другой , то вдруг, что то не то
X² + px + 6 = 0
D = p² - 24
√D = √(p² - 24)
![x = \frac{-pб \sqrt{p^2-24} }{2}](https://tex.z-dn.net/?f=x+%3D++%5Cfrac%7B-p%D0%B1+%5Csqrt%7Bp%5E2-24%7D+%7D%7B2%7D+)
![x_1^2+x_2^2 = ( \frac{-p+ \sqrt{p^2-24} }{2})^2+ ( \frac{-p- \sqrt{p^2-24} }{2})^2 = \\ \\ = \frac{( \sqrt{p^2-24}-p)^2 }{4}+ \frac{(-p- \sqrt{p^2-24})^2 }{4}= \frac{( \sqrt{p^2-24}-p)^2 +(-p- \sqrt{p^2-24})^2}{4} = \\ \\ = \frac{p^2-24-2p\sqrt{p^2-24}+p^2+p^2+2p\sqrt{p^2-24}+p^2-24}{4} = \frac{4p^2-48}{4}=p^2-12](https://tex.z-dn.net/?f=x_1%5E2%2Bx_2%5E2+%3D+%28+%5Cfrac%7B-p%2B+%5Csqrt%7Bp%5E2-24%7D+%7D%7B2%7D%29%5E2%2B+%28+%5Cfrac%7B-p-+%5Csqrt%7Bp%5E2-24%7D+%7D%7B2%7D%29%5E2+%3D++%5C%5C++%5C%5C++%3D+%5Cfrac%7B%28+%5Csqrt%7Bp%5E2-24%7D-p%29%5E2+%7D%7B4%7D%2B++%5Cfrac%7B%28-p-+%5Csqrt%7Bp%5E2-24%7D%29%5E2+%7D%7B4%7D%3D+%5Cfrac%7B%28+%5Csqrt%7Bp%5E2-24%7D-p%29%5E2+%2B%28-p-+%5Csqrt%7Bp%5E2-24%7D%29%5E2%7D%7B4%7D+%3D++%5C%5C++%5C%5C+%3D++%5Cfrac%7Bp%5E2-24-2p%5Csqrt%7Bp%5E2-24%7D%2Bp%5E2%2Bp%5E2%2B2p%5Csqrt%7Bp%5E2-24%7D%2Bp%5E2-24%7D%7B4%7D+%3D++%5Cfrac%7B4p%5E2-48%7D%7B4%7D%3Dp%5E2-12)
По условию сумма квадратов корней уравнения равна 40
p² - 12 = 40
p² = 52
p = +-√52
p = +-2√13
1. p = -2√13D = 52 - 24 = 28
√D = 2√7
![x = \frac{2 \sqrt{13} б2 \sqrt{7} }{2} = \sqrt{13} б \sqrt{7}](https://tex.z-dn.net/?f=x+%3D++%5Cfrac%7B2+%5Csqrt%7B13%7D+%D0%B12+%5Csqrt%7B7%7D+%7D%7B2%7D+%3D+%5Csqrt%7B13%7D+%D0%B1+%5Csqrt%7B7%7D+)
![x_1-x_2 = \sqrt{13} - \sqrt{7} - (\sqrt{13} + \sqrt{7}) = -2 \sqrt{7} \\ \\ x_2-x_1 = \sqrt{13} + \sqrt{7} - ( \sqrt{13} - \sqrt{7} ) =2 \sqrt{7}](https://tex.z-dn.net/?f=x_1-x_2+%3D+%5Csqrt%7B13%7D+-+%5Csqrt%7B7%7D+-+%28%5Csqrt%7B13%7D+%2B+%5Csqrt%7B7%7D%29+%3D+-2+%5Csqrt%7B7%7D++%5C%5C++%5C%5C+x_2-x_1+%3D+%5Csqrt%7B13%7D+%2B+%5Csqrt%7B7%7D+-+%28+%5Csqrt%7B13%7D+-+%5Csqrt%7B7%7D+%29++%3D2+%5Csqrt%7B7%7D+)
2.
p = 2√13D = 52 - 24 = 28
√D = 2√7
![x = \frac{-2 \sqrt{13} б2 \sqrt{7} }{2} =- \sqrt{13} б \sqrt{7}](https://tex.z-dn.net/?f=x+%3D+%5Cfrac%7B-2+%5Csqrt%7B13%7D+%D0%B12+%5Csqrt%7B7%7D+%7D%7B2%7D+%3D-+%5Csqrt%7B13%7D+%D0%B1+%5Csqrt%7B7%7D)
![OTBET: б2 \sqrt{7}](https://tex.z-dn.net/?f=OTBET%3A+%D0%B12+%5Csqrt%7B7%7D+)
1/2*ху=24
х^2+y^2=10^2
-------------------
xy=48
x^2+y^2=100
--------------------
x=48/y
(48/y)^2+y^2=100
--------------------------
2304/y^2+y^2=100 *y^2 если у^2 неравен 0
2304+y^4-100y^2=0
y^2=t t>=0
t^2-100t+2304=0
D=784
t1=(100+28)/2=64
t2=(100-28)/2=36
y^2=36 y^2=64
y1=6 y2=8
x1=8 x2=6
ответ 6и8
-3x + 5x = 24
2x = 24
x = 12