Lg(5(x-4))<1. одз:(х-4)>0
5(x-4)<10. х>4
x-4<2
x<6
ответ: 4<х<6
Sin²(180-x)=(sin(180-x))²=(sinx)²=sin²x=1-cos²x
cos(180-x)=-cosx
(1-cos²x)+2*(-cosx)+2=0
cos²x+2cosx-3=0
замена переменных:
cosx=t, t∈[-1;1]
t²+2t-3=0
D=16
t₁=1, t₂=-3. -3∉[-1;1]. t=-3 не подходит
обратная замена:
t=1
cosx=1, x=2πn, n∈Z
![2 \sqrt{10}= \sqrt{2^2*10}= \sqrt{4*10}= \sqrt{40} \\\\6,5= \sqrt{6,5^2}= \sqrt{42,25} \\\\ \sqrt{41} \\\\ \sqrt{42,25} > \sqrt{41}> \sqrt{40} \\\\6,5> \sqrt{41}> 2\sqrt{10}](https://tex.z-dn.net/?f=2+%5Csqrt%7B10%7D%3D+%5Csqrt%7B2%5E2%2A10%7D%3D+%5Csqrt%7B4%2A10%7D%3D+%5Csqrt%7B40%7D++%5C%5C%5C%5C6%2C5%3D+%5Csqrt%7B6%2C5%5E2%7D%3D+%5Csqrt%7B42%2C25%7D+%5C%5C%5C%5C+%5Csqrt%7B41%7D+%5C%5C%5C%5C+%5Csqrt%7B42%2C25%7D+%3E+%5Csqrt%7B41%7D%3E+%5Csqrt%7B40%7D+%5C%5C%5C%5C6%2C5%3E+%5Csqrt%7B41%7D%3E+2%5Csqrt%7B10%7D++++++)
Ответ: 6,5; <span>√41; </span><span>2<span>√10</span></span>