Sinx(1+2cosx)-cosx(1+2cosx)=0
1+2cosx=0⇒cosx=-1/2⇒x=+-2π/3+2πn
sinx-cosx=0
sinx-sin(π/2-x)=0
2sin(x-π/4)cosπ/4=0
sin(x-π/4)=0
x-π/4=πn
x=π/4+πn
x=п/4
Пусть задумали число x, тогда
3x + 2,6 = 4,4
3x = 4,4 - 2,6
3x = 1,8
x = 0,6
Задумали число 0,6
![1)\; \; \sqrt{4x^2+5x-2}=2\\\\4x^2+5x-2=4\\\\4x^2+5x-6=0\\\\D=25+96=121\\\\x_1=\frac{-5-11}{8}=-2\\\\x_2=\frac{-5+11}{8}=\frac{6}{8}=\frac{3}{4}\\\\Proerka:\; x=-2\; ,\; \sqrt{16-10-2}=\sqrt4=2\; ;\; \; 2=2\\\\x=\frac{3}{4}\; ,\; \sqrt{\frac{9}{4}+\frac{15}{4}-2}=\sqrt{6-2}=2\; ,\; \; 2=2](https://tex.z-dn.net/?f=1%29%5C%3B%20%5C%3B%20%5Csqrt%7B4x%5E2%2B5x-2%7D%3D2%5C%5C%5C%5C4x%5E2%2B5x-2%3D4%5C%5C%5C%5C4x%5E2%2B5x-6%3D0%5C%5C%5C%5CD%3D25%2B96%3D121%5C%5C%5C%5Cx_1%3D%5Cfrac%7B-5-11%7D%7B8%7D%3D-2%5C%5C%5C%5Cx_2%3D%5Cfrac%7B-5%2B11%7D%7B8%7D%3D%5Cfrac%7B6%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D%5C%5C%5C%5CProerka%3A%5C%3B%20x%3D-2%5C%3B%20%2C%5C%3B%20%5Csqrt%7B16-10-2%7D%3D%5Csqrt4%3D2%5C%3B%20%3B%5C%3B%20%5C%3B%202%3D2%5C%5C%5C%5Cx%3D%5Cfrac%7B3%7D%7B4%7D%5C%3B%20%2C%5C%3B%20%5Csqrt%7B%5Cfrac%7B9%7D%7B4%7D%2B%5Cfrac%7B15%7D%7B4%7D-2%7D%3D%5Csqrt%7B6-2%7D%3D2%5C%3B%20%2C%5C%3B%20%5C%3B%202%3D2)
![\sqrt{23+3x-5x^2}=3\\\\23+3x-5x^2=9\\\\5x^2-3x-14=0\\\\D=9+280=289\\\\x_1=\frac{3-17}{10}=-1,4\\\\x_2=\frac{3+17}{10}=2\\\\Proverka;\; \; x=2,\; \; \sqrt{23+6-20}=3,\; 3=3\\\\x=-1,4,\; \sqrt{23-4,2-9,8}=\sqrt{9}=3,\; \; 3=3](https://tex.z-dn.net/?f=%5Csqrt%7B23%2B3x-5x%5E2%7D%3D3%5C%5C%5C%5C23%2B3x-5x%5E2%3D9%5C%5C%5C%5C5x%5E2-3x-14%3D0%5C%5C%5C%5CD%3D9%2B280%3D289%5C%5C%5C%5Cx_1%3D%5Cfrac%7B3-17%7D%7B10%7D%3D-1%2C4%5C%5C%5C%5Cx_2%3D%5Cfrac%7B3%2B17%7D%7B10%7D%3D2%5C%5C%5C%5CProverka%3B%5C%3B%20%5C%3B%20x%3D2%2C%5C%3B%20%5C%3B%20%5Csqrt%7B23%2B6-20%7D%3D3%2C%5C%3B%203%3D3%5C%5C%5C%5Cx%3D-1%2C4%2C%5C%3B%20%5Csqrt%7B23-4%2C2-9%2C8%7D%3D%5Csqrt%7B9%7D%3D3%2C%5C%3B%20%5C%3B%203%3D3)
Можно было проверку и не делать и не находить ОДЗ, т.к. правые и левые части равенств ПОЛОЖИТЕЛЬНЫЕ числа.Поэтому при возведении в квадрат мы не получим посторонних корней.
<span>(13c-11d)*(13c+11d)=169c</span>²-121d²
(a-b)(a+b)=a²-b²