2^(x+1)+4^x=80 решите систему уравнений !

2*2^x + 2^(2x) - 80 = 0 

Пусть t = 2^x, тогда 
t^2 + 2t - 80 = 0 
D  = 4 + 4*80 = 324 = 18^2
t1 = ( - 2 + 18)/2 = 16/2 = 8;
t2 = ( - 2 - 18)/2 = - 20/2 = - 10 ==> не подходит

2^x = 8 
2^x = 2^3
x = 3 

1) cos х = sin² х cos х
cosx=0   x=+-π/2+2πn
cosx≠0    sin²x=1  sinx=+-1  x=+-π/2+πn
ответ:  x=+-π/2+πn

2)  2sinx = 3sin2x
2sinx = 3*2sinx cosx
sinx = 3sinx cosx
sinx=0  x=πn
1= 3cosx  cosx=1/3  x=+-arccos(1/3)+2πn
ответ:  x=πn и x=+-arccos(1/3)+2πn

3)  sin 2x = sin x
2sinx cosx=sinx
sinx=0  x=πn
2cosx=1
cosx=1/2    x=+-π/3 +2πn
ответ:  x=πn и x=+-π/3 +2πn

4) cos² 4х + cos 4x = 0
cos4x(cos4x+1)=0
cos4x=0     4x=+-π/2+πn    x=+-π/8+πn/4
cos4x+1=0    cos4x=-1    4x=+-πn+2πn   x=+-πn/4+πn/2
ответ: x=+-π/8+πn/4 и x=+-πn/4+πn/2

1. 9 —(8x — 11) = 12
9 — 8x + 11 = 12
—8x = 12 — 20 = —8; x = 1;

2. (6x + 1) —(3 — 2x) = 14
6x + 1 — 3 + 2x = 14
6x + 2x = 14 + 2
8x = 16; x = 2;

3. 2x —(6x — 5) = 45
2x — 6x + 5 = 45
2x — 6x = 45 — 5
—4x = 40; x = —10;

4. 5x —(7x + 7) = 9
5x — 7x — 7 = 9
5x — 7x = 9 + 7
—2x = 16; x = —8;

5. 2x —(6x + 1) = 9
2x — 6x — 1 = 9
2x — 6x = 9 + 1
—4x = 10; x = —2,5;

6. 4x —(7x — 2) = 17
4x — 7x + 2 = 17
4x — 7x = 17 — 2
—3x = 15; x = —5; 

7. 2x + 7 = 3x — 2 * (3x — 1)
2x + 7 = 3x — 6x + 2
2x — 3x + 6x = 2 — 7
5x = —5; x = —1;

8. 4 — 2 * (x + 3) = 4 * (x — 5)
4 — 2x — 6 = 4x — 20
—2x — 4x = —20 — 4 + 6
—6x = —18; x = 3;

9. 5x + 3 = 7x — 5 * (2x + 1)
5x + 3 = 7x — 10x — 5
5x — 7x + 10x = —5 — 3
8x = —8; x = —1;

10. 3y —(5 — y) = 11
3y — 5 + y = 11
3y + y = 11 + 5
4y = 16; y = 4.