<span>(k-3)(2k+1)=k*2k+1*k-3*2k-3*1=2k</span>²+k-6k-3=2k²-5k-3
<span>(3a-2)^2+(1+3a)(1-3a) = 9a</span>² - 12a + 4 + 1 - 9a² = 5 - 12a
см.вложение
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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
1) 9m⁶-169n⁶ = (3m³)² - (13n³)² = (3m³-13n³)(3m³+13n³)
2) 0,01m⁶ - 1 = (0,1m³)² - 1² = (0,1-m³)(0,1+m³)
3) 8m⁶ - 0,125n³ = (2m²)³ - (0,5n)³ = (2m² - 0,5n)(4m⁴+m²n+0,25n²)
4) a³ + 0,064b³ = a³ + (0,4b)³ = (a+0,4b)(a²-0,4ab+0,16b²)