![\sqrt{x+7}-\sqrt{5x+39}=-4](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B7%7D-%5Csqrt%7B5x%2B39%7D%3D-4)
возводим обе части в квадрат:
![x+7-2\sqrt{(5x+39)(x+7)}+5x+39=16 \\-2\sqrt{5x^2+74x+273}=-6x-30 \\\sqrt{5x^2+74x+273}=3x+15](https://tex.z-dn.net/?f=x%2B7-2%5Csqrt%7B%285x%2B39%29%28x%2B7%29%7D%2B5x%2B39%3D16%0A%5C%5C-2%5Csqrt%7B5x%5E2%2B74x%2B273%7D%3D-6x-30%0A%5C%5C%5Csqrt%7B5x%5E2%2B74x%2B273%7D%3D3x%2B15)
возводим еще раз в квадрат обе части:
![5x^2+74x+273=(3x+15)^2 \\5x^2+74x+273=9x^2+90x+225 \\4x^2+16x-48=0 \\x^2+4x-12=0](https://tex.z-dn.net/?f=5x%5E2%2B74x%2B273%3D%283x%2B15%29%5E2%0A%5C%5C5x%5E2%2B74x%2B273%3D9x%5E2%2B90x%2B225%0A%5C%5C4x%5E2%2B16x-48%3D0%0A%5C%5Cx%5E2%2B4x-12%3D0)
но:
![x+7 \geq 0](https://tex.z-dn.net/?f=x%2B7+%5Cgeq+0)
и
![5x+39 \geq 0](https://tex.z-dn.net/?f=5x%2B39+%5Cgeq+0)
и
![5x^2+74x+273 \geq 0](https://tex.z-dn.net/?f=5x%5E2%2B74x%2B273+%5Cgeq+0)
и
![3x+15 \geq 0](https://tex.z-dn.net/?f=3x%2B15+%5Cgeq+0)
![x^2+4x-12=0 \\D=16+48=64=8^2 \\x_1= \frac{-4+8}{2} =2 \\x_2=\frac{-4-8}{2}=-6](https://tex.z-dn.net/?f=x%5E2%2B4x-12%3D0%0A%5C%5CD%3D16%2B48%3D64%3D8%5E2%0A%5C%5Cx_1%3D+%5Cfrac%7B-4%2B8%7D%7B2%7D+%3D2%0A%5C%5Cx_2%3D%5Cfrac%7B-4-8%7D%7B2%7D%3D-6)
проверяем:
(-6)
![-6+7 \geq 0 \\-30+39 \geq 0 \\-18+15 \geq 0](https://tex.z-dn.net/?f=-6%2B7+%5Cgeq+0%0A%5C%5C-30%2B39+%5Cgeq+0%0A%5C%5C-18%2B15+%5Cgeq+0)
- неверно, посторонний корень.
(2)
![2+7 \geq 0 \\10+39 \geq 9 \\6+15 \geq 0 \\5*4+74*2+273 \geq 0](https://tex.z-dn.net/?f=2%2B7+%5Cgeq+0%0A%5C%5C10%2B39+%5Cgeq+9%0A%5C%5C6%2B15+%5Cgeq+0%0A%5C%5C5%2A4%2B74%2A2%2B273+%5Cgeq+0)
- верно, значит 2 - корень уравнения
Ответ: x=2
CAK, KAD, DAB, CAD, KAB, CAB.
Если стороны КА=ВА, то треугольник КАВ - равносторонний.
Ширина 9 см, длина на 4 см больше, значит, длина 9+4=13 см
Р=2(9+13)= 44 см
<u>Ответ: 44</u>
Дано АВСД-ромб
ВН-высота=19
<А=30°
Рассмотрим тр-к ABH
∠H=90°
<span> BH=AB * sin a</span>
AB=BH/sinα=19/sin30=19/0,5=38
<span>S(</span>ромба)=AD*BH=AB*BH=38*19=722