D(дискриминант) = b²-4ac
D=1296-1232=64⊃0. 2 корня
x1= 36+8/56=11/14
x2= 36-8/56=0.5
При a≥8; оригинале задаче пропущено.
![\sqrt{(\sqrt{a+4\sqrt{a-4}}-\sqrt{a-4\sqrt{a-4}})^2}=](https://tex.z-dn.net/?f=%5Csqrt%7B%28%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D%7D-%5Csqrt%7Ba-4%5Csqrt%7Ba-4%7D%7D%29%5E2%7D%3D)
![\sqrt{a+4\sqrt{a-4}-2\sqrt{a+4\sqrt{a-4}}\sqrt{a-4\sqrt{a-4}} +a-4\sqrt{a-4}}=](https://tex.z-dn.net/?f=%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D-2%5Csqrt%7Ba%2B4%5Csqrt%7Ba-4%7D%7D%5Csqrt%7Ba-4%5Csqrt%7Ba-4%7D%7D%20%2Ba-4%5Csqrt%7Ba-4%7D%7D%3D)
![\sqrt{2a-2\sqrt{a^2-16(a-4)}}=\sqrt{2a-2\sqrt{a^2-16a+64}}=\sqrt{2a-2\sqrt{(a-8)^2}}=\sqrt{2a-2(a-8)}}=\sqrt{2a-2a+16}}=\sqrt{16}=4](https://tex.z-dn.net/?f=%5Csqrt%7B2a-2%5Csqrt%7Ba%5E2-16%28a-4%29%7D%7D%3D%5Csqrt%7B2a-2%5Csqrt%7Ba%5E2-16a%2B64%7D%7D%3D%5Csqrt%7B2a-2%5Csqrt%7B%28a-8%29%5E2%7D%7D%3D%5Csqrt%7B2a-2%28a-8%29%7D%7D%3D%5Csqrt%7B2a-2a%2B16%7D%7D%3D%5Csqrt%7B16%7D%3D4)
В данном случае можно просто подставить нужное значение аргумента. (т.к. данная функция непрерывна в данной точке).
![\displaystyle \lim_{x\to -7} \frac{x+7}{ \sqrt{x+32-5} }= \frac{-7+7}{ \sqrt{-7+32-5} }= \frac{0}{ \sqrt{20} } =0](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Clim_%7Bx%5Cto+-7%7D+++%5Cfrac%7Bx%2B7%7D%7B+%5Csqrt%7Bx%2B32-5%7D+%7D%3D+%5Cfrac%7B-7%2B7%7D%7B++%5Csqrt%7B-7%2B32-5%7D+%7D%3D+%5Cfrac%7B0%7D%7B++%5Csqrt%7B20%7D+%7D++%3D0)
Легко.
1)2x^2 - 11x +12 = 0
a = 2, b = 11, c= 12
D = b^2-4ac=2^2 - 4 x 2 x 12 = -92
2) x^2 - 36x +324 = 0
a = 1, b = 36, c = 324
D = b^2-4ac=36^2-4 x 1 x 324 = 0
x1 = -b-корень D / 2a = -36 - 0 / 2 = -18