<span>(x²-5x+14)²-30</span><span>(x²-5x+6)</span>-40=0
<span>x²-5x+14=a
a²-30(a-8)-40=0
a²-30a+200=0
a1+a2=30 U a1*a2=200
a1=10⇒</span>x²-5x+14=10⇒<span>x²-5x+4=0⇒x1+x2=5 U x1*x2=4⇒x1=1 U x2=4
a2=20</span>⇒x²-5x+14=20⇒<span>x²-5x-6=0⇒x3+x4=5 U x3*x4=-6⇒x3=-1 U x2=6
x={-1;1;4;6}
</span>
Решение смотри в приложении
Ответ 2
![\frac{1}{ \sqrt{2}+1 } + \frac{1}{\sqrt{3}+\sqrt{2}} + \frac{1}{\sqrt{4}+\sqrt{3}} +...+ \frac{1}{\sqrt{20}+\sqrt{19}} =\\ \\ = \sqrt{2}-1+ \sqrt{3}- \sqrt{2}+ \sqrt{4}- \sqrt{3}+...+ \sqrt{20}- \sqrt{19}=-1+ \sqrt{20}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B+%5Csqrt%7B2%7D%2B1+%7D+%2B+%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%2B%5Csqrt%7B2%7D%7D+%2B+%5Cfrac%7B1%7D%7B%5Csqrt%7B4%7D%2B%5Csqrt%7B3%7D%7D+%2B...%2B+%5Cfrac%7B1%7D%7B%5Csqrt%7B20%7D%2B%5Csqrt%7B19%7D%7D+%3D%5C%5C+%5C%5C+%3D+%5Csqrt%7B2%7D-1%2B+%5Csqrt%7B3%7D-+%5Csqrt%7B2%7D%2B+%5Csqrt%7B4%7D-+%5Csqrt%7B3%7D%2B...%2B+%5Csqrt%7B20%7D-+%5Csqrt%7B19%7D%3D-1%2B+%5Csqrt%7B20%7D)
Очевидно., что
![16\ \textless \ 20\ \textless \ 25](https://tex.z-dn.net/?f=16%5C+%5Ctextless+%5C+20%5C+%5Ctextless+%5C+25+)
Тогда
![4\ \textless \ \sqrt{20} \ \textless \ 5\\ \\ 3\ \textless \ -1+ \sqrt{20}\ \textless \ 4](https://tex.z-dn.net/?f=4%5C+%5Ctextless+%5C++%5Csqrt%7B20%7D+%5C+%5Ctextless+%5C+5%5C%5C+%5C%5C+3%5C+%5Ctextless+%5C+-1%2B+%5Csqrt%7B20%7D%5C+%5Ctextless+%5C+4+)
Между соседними числа (3;4).