11.
Un=0+1+2+...+49
Sn =50.(0+49.1)/2=25.49=1225

12
0+1+..+n =120
(n+1).(0+n)/2 =120
n(n+1) =240 =15.16
n=15

13
1;3;5;...;(2n-1)
2.50-1 =99
số nguyên dương lẻ thứ 50 =99
S50 =50.(1+49.2)/2 =25.99 =2475

14
2x =15+47 =62
x=31

15
2(x^2 +1) =(x-1)+(5x-1)
2x^2 +2 =6x-2
x^2 -3x+2 =0
x={1 ;2}

16
u1+u2+u3 =21 (1)
u1^2 +u2^2+U3^2 =165(2)
csc (1) => u2 +2u2 =21 => u2 =7
(2) => u1^2 +u3^2 =165-7^2 = 116
(u1+u3)^2 =116+2u1.u3
(1)<=> u1+u3 =14(3)
<=>14^2 =116+2u1.u3
u1.u3 =(14^2 -116)/2 =40 (4)
(3)& (4) => u1 =4 ; u3 =10
ba số cần tìm : 4;7;10

17
A1;A2;A3
▲=> A1+A2+A3 =180
CSC=>A1+A3 =2A2
=>3 A2 =180
A2 =60^0
A1+A3 =120
A1+5/3 A1 =120
8A1/3 =120
A1 =120.3/8 =3.15 =45^0
ba góc ấy là : 45;60;75

18
x;y;z là 3 canh ▲; z=max(x;y;z;)
CV =x+y+z =12a (1)
▲vuông => z^2 =x^2+y^2 (2)
CSC => 2y=x+z
(1) => 3y =12a ;y=4a
z =12a-x-y =8a-x
z^2 =x^2 -16ax +64a
(2) =>x^2 -16ax +64a=x^2 +16a^2
<=> -16ax +64a= 16a^2
▲=> a >0
<=>- x+4 =a
x=4-a
x>0 => 0<a<4
ba canh là
4-a ; 4a ; 9a-4

19
CSC => 2b=a+c
a+b+c =15 => b=5; a+c=10
1/a+1/b+1/c =71/105
<=>1/a+ 1/c =71/105 -1/5 =10/21
<=>a+c=10/21 .ac
10=10/21 .ac
=> ac=21
ptdc : z^2 -10z+21=0
z=(3;7}
(a;b;c)=(3;5;7);(7;5;3)

11.
Un=0+1+2+...+49
u1 =0 ; d=1;n=50
Sn =n(u1+(n-1).d )/2 =50.(0+49.1)/2=25.49=1225