Объяснение:
{3*(x-1)-2*(1+x)<1 {3x-3-2-2x<1 {x-5<1 {x<6</p>
{3x-4≥0 {3x≥4 |÷3 {x≥4/3 {x≥4/3
Ответ: x∈[4/3;6).
2.
(√6+√3)*√12-2*√6*√3=√(6*12)+√(3*12)-√(4*6*3)=√72+√36-√72=√36=6.
3.
a) 3x²-11x+6=0 D=49 √D=7 x₁=3 x₂=2/3.
б) 4x²-1=0 (2x)²-1²=0 (2x+1)*(2x-1)=0 x₁=-1/2 x₂=1/2.
4.
![(\frac{6}{y^{2} -9}+\frac{1}{3-y})*\frac{y^{2}+6y+9 }{5}=(\frac{6}{(y+3)*(y-3)}-\frac{1}{y-3})* \frac{(y+3)^{2} }{5}=\frac{6-(y+3)}{(y+3)*(y-3)}* \frac{(y+3)^{2} }{5}=\\ =\frac{6-y-3}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\frac{3-y}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\frac{\\ -(y-3)}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\\ =-\frac{1}{(y+3)} * \frac{(y+3)^{2} }{5}=-\frac{(y+3)^{2} }{5*(y+3)}=-\frac{y+3}{5} . (\frac{6}{y^{2} -9}+\frac{1}{3-y})*\frac{y^{2}+6y+9 }{5}=(\frac{6}{(y+3)*(y-3)}-\frac{1}{y-3})* \frac{(y+3)^{2} }{5}=\frac{6-(y+3)}{(y+3)*(y-3)}* \frac{(y+3)^{2} }{5}=\\ =\frac{6-y-3}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\frac{3-y}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\frac{\\ -(y-3)}{(y+3)*(y-3)} * \frac{(y+3)^{2} }{5}=\\ =-\frac{1}{(y+3)} * \frac{(y+3)^{2} }{5}=-\frac{(y+3)^{2} }{5*(y+3)}=-\frac{y+3}{5} .](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%7D%7By%5E%7B2%7D%20-9%7D%2B%5Cfrac%7B1%7D%7B3-y%7D%29%2A%5Cfrac%7By%5E%7B2%7D%2B6y%2B9%20%7D%7B5%7D%3D%28%5Cfrac%7B6%7D%7B%28y%2B3%29%2A%28y-3%29%7D-%5Cfrac%7B1%7D%7By-3%7D%29%2A%20%20%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D%5Cfrac%7B6-%28y%2B3%29%7D%7B%28y%2B3%29%2A%28y-3%29%7D%2A%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D%5C%5C%20%20%20%3D%5Cfrac%7B6-y-3%7D%7B%28y%2B3%29%2A%28y-3%29%7D%20%2A%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D%5Cfrac%7B3-y%7D%7B%28y%2B3%29%2A%28y-3%29%7D%20%2A%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D%5Cfrac%7B%5C%5C%20-%28y-3%29%7D%7B%28y%2B3%29%2A%28y-3%29%7D%20%2A%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D%5C%5C%20%3D-%5Cfrac%7B1%7D%7B%28y%2B3%29%7D%20%2A%20%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%7D%3D-%5Cfrac%7B%28y%2B3%29%5E%7B2%7D%20%7D%7B5%2A%28y%2B3%29%7D%3D-%5Cfrac%7By%2B3%7D%7B5%7D%20%20%20.)
5.
a) 4¹¹*4⁻⁹=4⁽¹¹⁻⁹⁾=4²=16.
б) (2⁻²)³:2⁻⁵=2⁽⁻²*³⁾:2⁻⁵=2⁻⁶:2⁻⁵=2⁽⁻⁶⁻⁽⁻⁵⁾⁾=2⁽⁻⁶⁺⁵⁾=2⁻¹=1/2=0,5.