6(1-sin²x) -5√2sinx+2=0
6-6sin²x-5√2sinx+2=0
6sin²x +5√2sinx-8=0
sinx=t
6t² +5√2t-8=0
D=50+4*6*8=50+192=242
t1=(-5√2+11√2)/12=√2/2
t2=-16√2/12=-4√2/3
sinx=√2/2 sinx= -4√2/3 не подходит |sinx|≤1
x=П/4+2ПК
х=3П/4+2ПК
ОДЗ: х∈[-1;1]
![arccosx- \pi =arcsin \frac{4x}{3} \\ -( \pi -arccosx)=arcsin \frac{4x}{3} \\ \\ -arccos(-x)=arcsin \frac{4x}{3} \\ \\ sin(-arccos(-x))=sin(arcsin \frac{4x}{3} ) \\ \\-sin(arccos(-x))= \frac{4x}{3} \\ \\ - \sqrt{1-cos^2(arccos(-x))}=\frac{4x}{3} \\ \\ - \sqrt{1-(-x)^2} = \frac{4x}{3} \\ \\ - \sqrt{1- x^{2} } =\frac{4x}{3}](https://tex.z-dn.net/?f=arccosx-+%5Cpi+%3Darcsin+%5Cfrac%7B4x%7D%7B3%7D+%5C%5C+-%28+%5Cpi+-arccosx%29%3Darcsin+%5Cfrac%7B4x%7D%7B3%7D+%5C%5C+%5C%5C+-arccos%28-x%29%3Darcsin+%5Cfrac%7B4x%7D%7B3%7D+%5C%5C+%5C%5C+sin%28-arccos%28-x%29%29%3Dsin%28arcsin+%5Cfrac%7B4x%7D%7B3%7D+%29+%5C%5C+%5C%5C-sin%28arccos%28-x%29%29%3D+%5Cfrac%7B4x%7D%7B3%7D+++%5C%5C++%5C%5C+-+%5Csqrt%7B1-cos%5E2%28arccos%28-x%29%29%7D%3D%5Cfrac%7B4x%7D%7B3%7D+%5C%5C+%5C%5C++-+%5Csqrt%7B1-%28-x%29%5E2%7D+%3D+%5Cfrac%7B4x%7D%7B3%7D++%5C%5C++%5C%5C+-+%5Csqrt%7B1-+x%5E%7B2%7D+%7D+%3D%5Cfrac%7B4x%7D%7B3%7D)
![\sqrt{1-x^2} =- \frac{4x}{3} \ \ \ \textless \ =\ \textgreater \ \ \left \{ {{- \frac{4x}{3} \geq 0\ \ |*(-3)} \atop {1-x^2= \frac{16x^2}{9}|*9 }} \right. \\ \\ \left \{ {{4x \leq 0} \atop {9-9x^2=16 x^{2} }} \right. \ \ \ \textless \ =\ \textgreater \ \left \{ {{x \leq 0} \atop {16 x^{2} +9x^2-9=0}} \right. \\ \\ 16 x^{2} +9x^2-9=0 \\ \\25x^2=9\\ \\x^2= \frac{9}{25} \\ \\ x=^+_- \frac{3}{5} =^+_- 0.6](https://tex.z-dn.net/?f=%5Csqrt%7B1-x%5E2%7D+%3D-+%5Cfrac%7B4x%7D%7B3%7D+%5C+%5C++%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+%5C++%5Cleft+%5C%7B+%7B%7B-+%5Cfrac%7B4x%7D%7B3%7D+%5Cgeq+0%5C+%5C++%7C%2A%28-3%29%7D+%5Catop+%7B1-x%5E2%3D+%5Cfrac%7B16x%5E2%7D%7B9%7D%7C%2A9+%7D%7D+%5Cright.++%5C%5C++%5C%5C++%5Cleft+%5C%7B+%7B%7B4x+%5Cleq+0%7D+%5Catop+%7B9-9x%5E2%3D16+x%5E%7B2%7D+%7D%7D+%5Cright.+%5C+%5C+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++%5Cleft+%5C%7B+%7B%7Bx+%5Cleq+0%7D+%5Catop+%7B16+x%5E%7B2%7D+%2B9x%5E2-9%3D0%7D%7D+%5Cright.++%5C%5C++%5C%5C+16+x%5E%7B2%7D+%2B9x%5E2-9%3D0+%5C%5C++%5C%5C25x%5E2%3D9%5C%5C+%5C%5Cx%5E2%3D+%5Cfrac%7B9%7D%7B25%7D++%5C%5C++%5C%5C+x%3D%5E%2B_-+%5Cfrac%7B3%7D%7B5%7D+%3D%5E%2B_-+0.6)
С учетом ОДЗ и с учетом системы x≤0, подходит только корень -0,6
ОТВЕТ: -0,6
Y` = (х^3/7 - 2х)` = 3/7*х^(3/7-1) - 2 = 3/7*х^(-4/7) - 2 = 3 / (7*х^4/7) - 2
Y = -2x²
y= x
x = -2x²
x +2x² =0
x( 1+2x) =0
x = 0 1+2x =0
2x = -1
x = -1/2
x = -0.5
y =x
x =0 y =0
x = -0.5 y = -0.5
(0;0)
(-0,5; -0,5)
ответ С
10х+9=7х
10х-7х=-9
3х = -9
х = -3