2cos^2x + (2-<span>√2</span>)sinx+<span>√2</span>-2=0
cos^2x = 1 - sin^2x
2(1 - sin^2x) + (2-<span>√2</span>)sinx+<span>√2</span>-2=0
2-2sin^2x + (2-<span>√2</span>)sinx+<span>√2</span>-2=0
-2sin^2x+(2-<span>√2</span>)sinx+<span>√2</span>=0
2sin^2x-(2-<span>√2</span>)sinx-<span>√2</span>=0
D=(2-<span>√2</span>)^2 + 4*2*<span>√2</span> = 4 - 4<span>√2</span> + 2 + 8<span>√2</span> = 6+4<span>√2</span> = (<span>√2</span>+2)^2
sinx1=(2-<span>√2</span> - <span>√2</span>+2) /4 = (4-2 <span>√2</span>)/4 = (2- <span>√2</span>)/2 = <span>√2</span>/2 ->x=(-1)^(n+1) *pi/4+pi*n
sinx2 = (2-<span>√2</span> +<span>√2</span>+2) /4 = 1 ->x=pi/2+2pi*k
как-то так, проверььте
1) ...=х²+6х+9-(х²+9х)=х²+6х+9-х²-9х=-3х+9
2) ...=4n²+20n+15-20n-25=4n²-10
3) ...=a²+20a+100-a²-80a=100-60a
4) ...=9x²+12x+4+9x²-9x=18x²+3x+4
25х²-121≤0
25х²≤0+121
25х²≤121
х²=121/25
х²=4,84
х=плюс минус корень из 4,84
х=плюс 2,2 (минус отпадает, так как число из под корня всегда положительное)