3с 18 ч =72+18=90 часов
90-15=75часов
75часов-3 мин=74 часа 57 мин
А) (√6+√5)²-√120=(√6²+2√6√5+√5²)-√(4*30)=6+2√30+5-2√30=11
б) √60+(√5-√3)²=√(4*15)+(√5²-2√5√3+√3²)=2√15+5-2√15+3=8
в)
![( \sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}})^{2} =(\sqrt{2+\sqrt{3}})^{2}+2\sqrt{2+\sqrt{3}}\sqrt{2- \sqrt{3}}+](https://tex.z-dn.net/?f=%28+%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%2B%5Csqrt%7B2-%5Csqrt%7B3%7D%7D%29%5E%7B2%7D+%3D%28%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%29%5E%7B2%7D%2B2%5Csqrt%7B2%2B%5Csqrt%7B3%7D%7D%5Csqrt%7B2-+%5Csqrt%7B3%7D%7D%2B)
![( \sqrt{2- \sqrt{3}})^{2}=2+ \sqrt{3} +2\sqrt{(2+ \sqrt{3})(2- \sqrt{3}})+2- \sqrt{3} =](https://tex.z-dn.net/?f=%28+%5Csqrt%7B2-+%5Csqrt%7B3%7D%7D%29%5E%7B2%7D%3D2%2B+%5Csqrt%7B3%7D+%2B2%5Csqrt%7B%282%2B+%5Csqrt%7B3%7D%29%282-+%5Csqrt%7B3%7D%7D%29%2B2-+%5Csqrt%7B3%7D+%3D)
![4+2 \sqrt{2^{2}-\sqrt{3}^{2}}=4+2\sqrt{4-3} =4+2 \sqrt{1}=5](https://tex.z-dn.net/?f=4%2B2+%5Csqrt%7B2%5E%7B2%7D-%5Csqrt%7B3%7D%5E%7B2%7D%7D%3D4%2B2%5Csqrt%7B4-3%7D+%3D4%2B2+%5Csqrt%7B1%7D%3D5)
г)
![( \sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}})^{2}=](https://tex.z-dn.net/?f=%28+%5Csqrt%7B3%2B2%5Csqrt%7B2%7D%7D-%5Csqrt%7B3-2%5Csqrt%7B2%7D%7D%29%5E%7B2%7D%3D)
![3+2\sqrt{2}-2\sqrt{(3+2\sqrt{2})(3-2\sqrt{2})}+3-2\sqrt{2}=6-2\sqrt{3^{2}-(2 \sqrt{2})^{2}}=](https://tex.z-dn.net/?f=3%2B2%5Csqrt%7B2%7D-2%5Csqrt%7B%283%2B2%5Csqrt%7B2%7D%29%283-2%5Csqrt%7B2%7D%29%7D%2B3-2%5Csqrt%7B2%7D%3D6-2%5Csqrt%7B3%5E%7B2%7D-%282+%5Csqrt%7B2%7D%29%5E%7B2%7D%7D%3D)
![6-2 \sqrt{9-4*2}=6-2* \sqrt{1} =6-2=4](https://tex.z-dn.net/?f=6-2+%5Csqrt%7B9-4%2A2%7D%3D6-2%2A+%5Csqrt%7B1%7D+%3D6-2%3D4)
х²-3=(х+√3)(х-√3)
4у²-5=(2у+√5)(2у-√5)
2-с²=(√2+с)(√2-с)
4-а=(2+√а)(2-√а)
![\frac{ x^{2} -2}{x+ \sqrt{2} }= \frac{(x+ \sqrt{2})(x- \sqrt{2})}{x+ \sqrt{2}}=x- \sqrt{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B2%7D+-2%7D%7Bx%2B+%5Csqrt%7B2%7D+%7D%3D+%5Cfrac%7B%28x%2B+%5Csqrt%7B2%7D%29%28x-+%5Csqrt%7B2%7D%29%7D%7Bx%2B+%5Csqrt%7B2%7D%7D%3Dx-+%5Csqrt%7B2%7D)
![\frac{x-4}{ \sqrt{x} +2}= \frac{( \sqrt{x} +2)( \sqrt{x} -2)}{ \sqrt{x} +2} = \sqrt{x} -2](https://tex.z-dn.net/?f=+%5Cfrac%7Bx-4%7D%7B+%5Csqrt%7Bx%7D+%2B2%7D%3D+%5Cfrac%7B%28+%5Csqrt%7Bx%7D+%2B2%29%28+%5Csqrt%7Bx%7D+-2%29%7D%7B+%5Csqrt%7Bx%7D+%2B2%7D+%3D+%5Csqrt%7Bx%7D+-2)
![\frac{a- \sqrt{a} }{ \sqrt{a}-1 }= \frac{ \sqrt{a}( \sqrt{a}-1)}{ \sqrt{a}-1} = \sqrt{a} ](https://tex.z-dn.net/?f=+%5Cfrac%7Ba-+%5Csqrt%7Ba%7D+%7D%7B+%5Csqrt%7Ba%7D-1+%7D%3D+%5Cfrac%7B+%5Csqrt%7Ba%7D%28+%5Csqrt%7Ba%7D-1%29%7D%7B+%5Csqrt%7Ba%7D-1%7D+%3D+%5Csqrt%7Ba%7D+%0A)
![\frac{c \sqrt{c}+c}{c+ \sqrt{c} } = \frac{ \sqrt{c}(c+ \sqrt{c)}}{c+ \sqrt{c} } = \sqrt{c}](https://tex.z-dn.net/?f=+%5Cfrac%7Bc+%5Csqrt%7Bc%7D%2Bc%7D%7Bc%2B+%5Csqrt%7Bc%7D+%7D+%3D+%5Cfrac%7B+%5Csqrt%7Bc%7D%28c%2B+%5Csqrt%7Bc%29%7D%7D%7Bc%2B+%5Csqrt%7Bc%7D+%7D+%3D+%5Csqrt%7Bc%7D+)
54-46=8 м
ответ:
они находились друг от друга на расстоянии 8 метров
![{x}^{2} y + x {y}^{2} - 3 - x - y + 3xy = \\ = xy(x + y) - (x + y) + 3 (xy - 1) = \\ = (x + y)(xy - 1) + 3(xy - 1) = \\ = (xy - 1)(x + y + 3) \\ \\](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D+y+%2B+x+%7By%7D%5E%7B2%7D++-+3+-+x+-+y+%2B+3xy+%3D++%5C%5C++%3D+xy%28x+%2B+y%29+-+%28x+%2B+y%29++%2B+3+%28xy+-+1%29+%3D++%5C%5C++%3D+%28x+%2B+y%29%28xy+-+1%29++%2B++3%28xy+-+1%29+%3D++%5C%5C++%3D+%28xy+-+1%29%28x+%2B+y+%2B+3%29+%5C%5C++%5C%5C+)
x=1,75=1. 3/4=7/4
y=3/7
![( \frac{7}{4} \times \frac{3}{7} - 1)( \frac{7}{4} + \frac{3}{7} + 3) = \\ = - \frac{1}{4} \times \frac{49 + 12 + 84}{28} = \\ = - \frac{145}{28} = - 5 \frac{5}{28}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B7%7D%7B4%7D++%5Ctimes++%5Cfrac%7B3%7D%7B7%7D++-+1%29%28+%5Cfrac%7B7%7D%7B4%7D++%2B++%5Cfrac%7B3%7D%7B7%7D++%2B+3%29+%3D++%5C%5C++%3D++-++%5Cfrac%7B1%7D%7B4%7D++%5Ctimes++%5Cfrac%7B49+%2B+12+%2B+84%7D%7B28%7D++%3D++%5C%5C++%3D++-++%5Cfrac%7B145%7D%7B28%7D++%3D++-+5+%5Cfrac%7B5%7D%7B28%7D+)
Ответ: -5 целых 5/28
4)
![a {x}^{2} + bx + c = a(x - x_{1} )(x - x_{2} )](https://tex.z-dn.net/?f=a+%7Bx%7D%5E%7B2%7D++%2B+bx+%2B+c+%3D+a%28x+-+x_%7B1%7D+%29%28x+-+++x_%7B2%7D+%29)
![{x}^{2} - 5x + 6 = 0](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++-+5x+%2B+6+%3D+0)
по теореме Виета найдем корни уравнения:
![x_{1} + x_{2} = 5 \\ x_{1} \times x_{2} = 6 \\ x_{1} = 2 \\ x_{2} = 3 \\ a = 1](https://tex.z-dn.net/?f=+x_%7B1%7D+%2B++x_%7B2%7D+%3D+5+%5C%5C+x_%7B1%7D++%5Ctimes+++x_%7B2%7D+%3D+6+%5C%5C+x_%7B1%7D++%3D+2+%5C%5C+x_%7B2%7D+%3D+3+%5C%5C+a+%3D+1)
Ответ:
![{x}^{2} - 5x + 6 = (x - 2)(x - 3)](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D++-+5x+%2B+6+%3D+%28x+-+2%29%28x+-+3%29)
5)
![{x}^{2} + 29 = (x + 5)(x - 3) \\ {x}^{2} + 29 = {x}^{2} + 5x - 3x - 15 \\ 2x = 15 + 29 \\ 2x = 44 \\ x = 22](https://tex.z-dn.net/?f=+%7Bx%7D%5E%7B2%7D++%2B+29+%3D+%28x+%2B+5%29%28x+-+3%29+%5C%5C++%7Bx%7D%5E%7B2%7D++%2B+29+%3D++%7Bx%7D%5E%7B2%7D++%2B+5x+-+3x+-+15+%5C%5C+2x+%3D+++15+++%2B+29+%5C%5C+2x+%3D+44+%5C%5C+x+%3D+22)
Ответ: сторона квадрата равна 22.