1) 4(x-5)-(7x+9)=1
4x-20-7x-9=1
-3x=30x / (-3)
x= -10
3) 0.3(6x+1.5)=2.7x-0.6(x-2)
1.8x+0.45=2.7x-0.6x+1.2
1.8x-2.7x+0.6x=1.2-0.45
-0.3x=0.75 / (-0.3)
x= -2.5
7.
![f(x)=( \sqrt{x} + \frac{1}{ \sqrt{x} })^{40}=(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{40}](https://tex.z-dn.net/?f=f%28x%29%3D%28%20%5Csqrt%7Bx%7D%20%2B%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7Bx%7D%20%7D%29%5E%7B40%7D%3D%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B40%7D)
![f'(x)=((x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{40})'=40(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{39}*( \frac{1}{2}x^{ -\frac{1}{2} }- \frac{1}{2}x^{ -\frac{3}{2} } )=](https://tex.z-dn.net/?f=f%27%28x%29%3D%28%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B40%7D%29%27%3D40%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%20%5Cfrac%7B1%7D%7B2%7Dx%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29%3D)
![=20(x^{ \frac{1}{2} } +x^{ -\frac{1}{2} })^{39}*( x^{ -\frac{1}{2} }- x^{ -\frac{3}{2} } )](https://tex.z-dn.net/?f=%3D20%28x%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2Bx%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%20x%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%20x%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29)
![f'(1)=20(1^{ \frac{1}{2} } +1^{ -\frac{1}{2} })^{39}*( 1^{ -\frac{1}{2} }- 1^{ -\frac{3}{2} } )=0](https://tex.z-dn.net/?f=f%27%281%29%3D20%281%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%2B1%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D%29%5E%7B39%7D%2A%28%201%5E%7B%20-%5Cfrac%7B1%7D%7B2%7D%20%7D-%201%5E%7B%20-%5Cfrac%7B3%7D%7B2%7D%20%7D%20%29%3D0)
8. f(x)=(x-2)²(x+4)=(x²-4x+4)(x+4)=x³+4x²-4x²-16x+4x+16=x³-12x+16
f'(x)=3x²-12≤0
3x²≤12
x²≤4
x∈[-2;2]
a) P_{4} = 4! =1·2·3·4 = 24; б) = 1/40320; b)[tex]C^2_27 = \frac{27!}{2!(27! - 2!)} = 351;
C^2_26 ={26!}{2!(26! - 2!)} =50; 351 - 50 =301;
г) [tex]A^3_10 = \frac{10!}{(10 - 3)!} = 720; [tex]C^3_10 = \frac{10!}{3!(10-3)1} = 120; 720÷120 = ;6
<span>область определения функции</span>