(-x^2y^3)^3*(-2x^5y)^2=-4x^16y^11
(2a-3b)(5a+b)-10(a+b)=10a^2-13ab-3b^2-10a-10b
1) x^2-2x-24=0 при х≠-4
D=k^2-c, D=(-1)^2-(-24), D=25
x=-k±√D, x=1±√25, x₁=1-5=-4 - не подходит, х₂=1+5=6
Ответ: х=6
2) x^2-3x-28=0 при х≠4 и х≠-4
D=b^2-4ac, D=(-3)^2-4*1*(-28), D=9+112, D=121
x=(-b±√D)/2a, x=(3±√121)/2*1, x₁=(3-11)/2=-8/2=-4 - не подходит, х₂=(3+11)/2=14/2=7
Ответ: х=7
3) 2х^2+5х-3=0 при х≠-5 и х≠5
D=b^2-4ac, D=5^2-4*2*(-3), D=25+24, D=49
x=(-b±√D)/2a, x=(-5<span>±</span>√49)/2*2, x₁=(-5-7)/4=-12/4=-3, x₂=(-5+7)/4=2/4=1/2=0,5
Ответ: х=-3, х=0,5
Тема: "Преобразование произведения в сумму".
Три основные формулы, которыми будем пользоваться:
cosx*cosy=1/2(cos(x+y)+cos(x-y))
sinx*siny=1/2(cos(x-y)-cos(x+y))
sinx*cosy=1/2(sin(x+y)+sin(x-y))
sin82*30`*cos52*30`=1/2(sin(82*30`+52*30`)+sin(82*30`-52*30`))=
=1/2(sin135*+sin30*)=1/2sin135*+1/2*1/2=
=1/2sin(90*+45*)+1/4=1/2cos45*+1/4=![\frac{1}{2}*\frac{\sqrt{2}}{2}+\frac{1}{4}=\frac{\sqrt{2}+1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D%2B1%7D%7B4%7D)
sin82*30`*cos37*30`=1/2(sin(82*30`+37*30`)+sin(82*30`-37*30`)=
=1/2(sin120*+sin45*)=![\frac{1}{2}(\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2})=\frac{\sqrt{3}+\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%2B%5Csqrt%7B2%7D%7D%7B4%7D)
cos37*30`*cos7*30`=1/2(cos(37*30`-7*30`)+cos(37*30`+7*30`)=
1/2(cos30*+cos45*)=![\frac{1}{2}(\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2})=</p> <p>=\frac{\sqrt{3}+\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%3D%3C%2Fp%3E%0A%3Cp%3E%3D%5Cfrac%7B%5Csqrt%7B3%7D%2B%5Csqrt%7B2%7D%7D%7B4%7D)
cos75*cos105*=1/2(cos(75*+105*)+cos(105*-75*))=1/2(cos180*+cos30*)=
![=\frac{1}{2}(-1+\frac{\sqrt{3}}{2})=\frac{\sqrt{3}-2}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%28-1%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29%3D%5Cfrac%7B%5Csqrt%7B3%7D-2%7D%7B4%7D)
cos45*cos75*=1/2(cos(75*-45*)+cos(75*-45*))=1/2(cos120*+cos30*)=
![=\frac{1}{2}(-\frac{1}{2}+\frac{\sqrt{3}}{2})=\frac{\sqrt{3}-1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%28-%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29%3D%5Cfrac%7B%5Csqrt%7B3%7D-1%7D%7B4%7D)
Лови ответ) Если что будет непонятно-обращайся
(√5-√2)^2=5-2√10+2=7-2√10
Ответ: 3