((х^2-10х+25)/(х^2-25))^3:((х-5)/(х+5))^3=1
((х-5)^2 /(х-5)(х+5))^3:((х-5)/(х+5))^3=1
(х-5 / х+5 )^3 : (х-5 /х+5)^3 =1
(х-5 / х+5 )^0 =1
1=1
а^0=1
а^m :a^n =a^m-n у нас
а^3 :а^3=а^3-3 =а^0=1
80/240=х/300
2/6= х/300
х=2*300/6 =100 см
Ответ :на расстоянии 100 см
1)
одз:
x>=-5
решаем:
![x^4*\sqrt{x+5}=0 \\x^4=0 \\x_1=0 \\\sqrt{x+5}=0 \\x+5=0 \\x_2=-5](https://tex.z-dn.net/?f=x%5E4%2A%5Csqrt%7Bx%2B5%7D%3D0+%5C%5Cx%5E4%3D0+%5C%5Cx_1%3D0+%5C%5C%5Csqrt%7Bx%2B5%7D%3D0+%5C%5Cx%2B5%3D0+%5C%5Cx_2%3D-5)
Ответ: x1=0; x2=-5
2)
одз:
![x \geq -2 \\ x \geq 6 \\ x \in [6;+\infty)](https://tex.z-dn.net/?f=x+%5Cgeq+-2+%5C%5C+x+%5Cgeq+6+%5C%5C+x+%5Cin+%5B6%3B%2B%5Cinfty%29)
решаем:
![\sqrt{x+2}=2+\sqrt{x-6} \\\sqrt{x+2}-\sqrt{x-6}=2](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B2%7D%3D2%2B%5Csqrt%7Bx-6%7D+%5C%5C%5Csqrt%7Bx%2B2%7D-%5Csqrt%7Bx-6%7D%3D2)
возведем обе части в квадрат:
![x+2+x-6-2\sqrt{(x+2)(x-6)}=4 \\2x-4-2\sqrt{(x+2)(x-6)}=4 \\2\sqrt{(x+2)(x-6)}=2x-8 \\\sqrt{(x+2)(x-6)}=x-4](https://tex.z-dn.net/?f=x%2B2%2Bx-6-2%5Csqrt%7B%28x%2B2%29%28x-6%29%7D%3D4+%5C%5C2x-4-2%5Csqrt%7B%28x%2B2%29%28x-6%29%7D%3D4+%5C%5C2%5Csqrt%7B%28x%2B2%29%28x-6%29%7D%3D2x-8+%5C%5C%5Csqrt%7B%28x%2B2%29%28x-6%29%7D%3Dx-4)
еще раз возведем в квадрат:
![(x+2)(x-6)=(x-4)^2 \\x^2-6x+2x-12=x^2-8x+16 \\-4x-12=-8x+16 \\4x=12+16 \\4x=28 \\x=7 \in [6;+\infty)](https://tex.z-dn.net/?f=%28x%2B2%29%28x-6%29%3D%28x-4%29%5E2+%5C%5Cx%5E2-6x%2B2x-12%3Dx%5E2-8x%2B16+%5C%5C-4x-12%3D-8x%2B16+%5C%5C4x%3D12%2B16+%5C%5C4x%3D28+%5C%5Cx%3D7+%5Cin+%5B6%3B%2B%5Cinfty%29)
Ответ: x=7