Прикрепляю....................................
Lg²x-3(lg10+lgx)-1=0 lg(10x) заменили на (lg10+ lgх), а lg10=1
lg²x-3lgx-3-1=0
lg²x-3lgx-4=0 сделаем замену пусть lgx=t
t²-3t-4=0
D=9+16=25
t₁=3-5/2=-1 t₂=3+5/2=4 сделаем обратную замену
lgx=-1, x=1/10
lgx=4 x=10⁴, x=10000
9х-9х+2=0
9х-9х=-2
9х-9х=0 =>
х=-2
Производную ищем, как производную произведения.
![f'(x)=( (x-1)* \sqrt{x+1} )'=( (x-1)* (x+1)^{ \frac{1}{2} } )'= \\ =(x-1)' *(x+1)^{ \frac{1}{2} } +(x-1)*((x+1)^{ \frac{1}{2} } )'= \\ =1*(x+1)^{ \frac{1}{2} } +(x-1)*\frac{1}{2}*(x+1)^{ -\frac{1}{2} } = \\ =(x+1)^{ \frac{1}{2} } +\frac{1}{2} *(x-1)* \frac{1}{(x+1)^{ \frac{1}{2} }} = \sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28+%28x-1%29%2A+%5Csqrt%7Bx%2B1%7D++%29%27%3D%28+%28x-1%29%2A+%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D+%5C%5C+%3D%28x-1%29%27+%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%28%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D++%5C%5C+%3D1%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%5Cfrac%7B1%7D%7B2%7D%2A%28x%2B1%29%5E%7B+-%5Cfrac%7B1%7D%7B2%7D+%7D+%3D++%5C%5C+%3D%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%5Cfrac%7B1%7D%7B2%7D+%2A%28x-1%29%2A+%5Cfrac%7B1%7D%7B%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D%7D+%3D+%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+)
Подставляем x = 3
![\sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}} = \sqrt{3+1} + \frac{3-1}{2 \sqrt{3+1} } =2+ \frac{1}{2} =2,5](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+%3D+%5Csqrt%7B3%2B1%7D+%2B+%5Cfrac%7B3-1%7D%7B2+%5Csqrt%7B3%2B1%7D+%7D+%3D2%2B+%5Cfrac%7B1%7D%7B2%7D+%3D2%2C5)