Уравнение
![x^2+48=0](https://tex.z-dn.net/?f=x%5E2%2B48%3D0)
не имеет решения, т.к. х²≥0 и 48>0. Их сумма не может быть = 0.
Ответ: х∈∅ .
Разложить на множители:
![x^2+48=x^2+2\sqrt{48}x+48-2\sqrt{48}x=(x+\sqrt{48})^2-2\sqrt{48}x=\\\\=(x+\sqrt{48}-\sqrt[4]{48}\cdot \sqrt{2x})(x+\sqrt{48}+ \sqrt[4]{48}\cdot \sqrt{2x})=\\\\=(x+4\sqrt3-2\sqrt[4]3\cdot \sqrt{2x})(x+4\sqrt3+2 \sqrt[4]{3}\cdot \sqrt{2x})](https://tex.z-dn.net/?f=x%5E2%2B48%3Dx%5E2%2B2%5Csqrt%7B48%7Dx%2B48-2%5Csqrt%7B48%7Dx%3D%28x%2B%5Csqrt%7B48%7D%29%5E2-2%5Csqrt%7B48%7Dx%3D%5C%5C%5C%5C%3D%28x%2B%5Csqrt%7B48%7D-%5Csqrt%5B4%5D%7B48%7D%5Ccdot+%5Csqrt%7B2x%7D%29%28x%2B%5Csqrt%7B48%7D%2B+%5Csqrt%5B4%5D%7B48%7D%5Ccdot+%5Csqrt%7B2x%7D%29%3D%5C%5C%5C%5C%3D%28x%2B4%5Csqrt3-2%5Csqrt%5B4%5D3%5Ccdot+%5Csqrt%7B2x%7D%29%28x%2B4%5Csqrt3%2B2+%5Csqrt%5B4%5D%7B3%7D%5Ccdot+%5Csqrt%7B2x%7D%29)
1) 2х² <span>+ 5х - 7 = 0
D = 25 + 56 = 81
x</span>₁ =
![\frac{-5-9}{4} = - \frac{14}{4} = -3,5](https://tex.z-dn.net/?f=+%5Cfrac%7B-5-9%7D%7B4%7D+%3D+-+%5Cfrac%7B14%7D%7B4%7D+%3D+-3%2C5+)
<span>
x</span>₂ =
![\frac{-5+9}{4} = \frac{4}{4} = 1](https://tex.z-dn.net/?f=+%5Cfrac%7B-5%2B9%7D%7B4%7D+%3D+%5Cfrac%7B4%7D%7B4%7D+%3D+1+)
<span>
Два корня
2) 3х</span>² <span>- 7х - 8 = 0
</span>D = 49 + 96 = 145
<span>
x</span>₁ =
![\frac{7 + \sqrt{145}}{6} = 42 + \sqrt{145}](https://tex.z-dn.net/?f=+%5Cfrac%7B7+%2B+%5Csqrt%7B145%7D%7D%7B6%7D+%3D+42+%2B+%5Csqrt%7B145%7D)
<span>
x</span>₂ =
![\frac{7 - \sqrt{145}}{6} = 42 - \sqrt{145}](https://tex.z-dn.net/?f=+%5Cfrac%7B7+-+%5Csqrt%7B145%7D%7D%7B6%7D+%3D+42+-+%5Csqrt%7B145%7D)
<span>
Два корня
3) 4х</span>² <span>+ 4х + 1 = 0
D = 16 - 16 = 0
x</span>₁ =
![\frac{-4}{8} = - \frac{1}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B-4%7D%7B8%7D+%3D+-+%5Cfrac%7B1%7D%7B2%7D+)
<span>
Один корень
4) 9х</span>² - 6х + 2 = 0
D = 36 - 72 = -36
D < 0 (корней нет)
1)8а^9+36a^6b^2+54a^3b^4+27b^6
2)8m^6-36m^4n^2+54m^2n^4-27n^6
файл
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