У = √х
А(М; 1) - точка на графике
у = 1
√х = 1
х = 1
При М = 1, график проходит через точку А
Пусть число имеет вид 10(b+3)+b , тогда если :
b=0 ; число 30
b=1; число 41
b=2 число 52
b=3 число 63
b=4 число 74
b=5 число 85
b=6 число 96
1)![\left \{ {{x-y=4} \atop {xy=5}} \right.\\\left \{ {{x=4+y} \atop {(4+y)y=5}} \right.\\\left \{ {{x=4+y} \atop {y^2+4y-5=0}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx-y%3D4%7D+%5Catop+%7Bxy%3D5%7D%7D+%5Cright.%5C%5C%5Cleft+%5C%7B+%7B%7Bx%3D4%2By%7D+%5Catop+%7B%284%2By%29y%3D5%7D%7D+%5Cright.%5C%5C%5Cleft+%5C%7B+%7B%7Bx%3D4%2By%7D+%5Catop+%7By%5E2%2B4y-5%3D0%7D%7D+%5Cright.)
![y^2+4y-5=0\\D=16+20=36\\\sqrt{D}=6\\y_{1}=\frac{-4+6}{2}=1\\y_{2}=\frac{-4-6}{2}=-5](https://tex.z-dn.net/?f=y%5E2%2B4y-5%3D0%5C%5CD%3D16%2B20%3D36%5C%5C%5Csqrt%7BD%7D%3D6%5C%5Cy_%7B1%7D%3D%5Cfrac%7B-4%2B6%7D%7B2%7D%3D1%5C%5Cy_%7B2%7D%3D%5Cfrac%7B-4-6%7D%7B2%7D%3D-5)
y1=1 y2=-5
x1=4+1=5 x2=4-5=-1
2)![y\leq3x^2+1](https://tex.z-dn.net/?f=y%5Cleq3x%5E2%2B1)
y=1 y=-3
x=0 x=-3
3)d=9-2=7
a1=2
![a_{n}=a_{1}+(n-1)d\\a_{10}= 2+(10-1)*7=2+63=65\\S_{n}=\frac{2a_{1}+(n-1)d}{2}*n\\S_{20}=\frac{2*2+(20-1)*7}{2}*20=\frac{4+133}{2}*20=\frac{2740}{2}=1370](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7D%2B%28n-1%29d%5C%5Ca_%7B10%7D%3D+2%2B%2810-1%29%2A7%3D2%2B63%3D65%5C%5CS_%7Bn%7D%3D%5Cfrac%7B2a_%7B1%7D%2B%28n-1%29d%7D%7B2%7D%2An%5C%5CS_%7B20%7D%3D%5Cfrac%7B2%2A2%2B%2820-1%29%2A7%7D%7B2%7D%2A20%3D%5Cfrac%7B4%2B133%7D%7B2%7D%2A20%3D%5Cfrac%7B2740%7D%7B2%7D%3D1370)
4)Т.к. угол 1 четверти, тогда значения sin , cos положительные.
5) ![b_{n}^2=b_{n-1}*b_{n+1}\\b_{3}^2=b_{3-1}*b_{3+1}=b_2*b_4=16*256\\b_3=\sqrt{16*256}=64\\q=\frac{b_3}{b_2}=\frac{64}{16}=4\\b_1=\frac{b_2}{q}=\frac{16}{4}=4](https://tex.z-dn.net/?f=b_%7Bn%7D%5E2%3Db_%7Bn-1%7D%2Ab_%7Bn%2B1%7D%5C%5Cb_%7B3%7D%5E2%3Db_%7B3-1%7D%2Ab_%7B3%2B1%7D%3Db_2%2Ab_4%3D16%2A256%5C%5Cb_3%3D%5Csqrt%7B16%2A256%7D%3D64%5C%5Cq%3D%5Cfrac%7Bb_3%7D%7Bb_2%7D%3D%5Cfrac%7B64%7D%7B16%7D%3D4%5C%5Cb_1%3D%5Cfrac%7Bb_2%7D%7Bq%7D%3D%5Cfrac%7B16%7D%7B4%7D%3D4)