George Washington was the first American president.
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
ОДЗ:
а) x² -6≥0
(x-√6)(x+√6)≥0
x=√6 x= -√6
+ - +
------- -√6 ------------ √6 ------------
\\\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-∞; -√6]U[√6; +∞)
b) 3-x≥0
-x≥ -3
x≤3
В итоге ОДЗ: х∈(-∞; -√6]U[√6; 3]
x²-6=(3-x)²
x²-6=9-6x+x²
x²-x²+6x=9+6
6x=15
x=15 : 6
x=2.5
Ответ: 2,5