1
log(5)1/25+log(√3)27=-2+6=4
2
log(0,5)4+log(√5)25=-2+4=2
3
2^(2x-4)=9
2x-4=log(2)9
2x=4+2log(2)3
x=2+log(2)3
4
5^(3x+6)=27
3x+6=log(5)27
3x=-6+3log(5)3
x=-2+log(5)3
A/b=3a^2/3aba/b=-a^2 /-aba/b= a3b /a2b2a/b= a2 /aba/b=5a3b /5a2b2 x/2y=2x /4yx/2y=xy /2y2x/2y= 2x2 /4xyx/2y=3 x3 y / 6x2y2<span>x/2y= 4xy /8y3</span>
Sin(arccos3/5)cos(arcsin8/17)+cos(arccos3/5)sin(arcsin8/17)=
sin(arcsin(√(1-(3/5)²)))cos(arccos(√(1-(8/17)²)))+3/5*8/17=
sin(arcsin4/5)cos(arccos15/17)+24/85=4/5*15/17+24/85=60/85+24/85=84/85
![6cos^2x-5sinx+1=0 \\ 6(1-sin^2x)-5sinx+1=0 \\ 6-6sin^2x-5sinx+1=0 \\ -6sin^2x-5sinx+7=0(*-1) \\ 6sin^2x+5sinx-7=0 \\ D=25+168=193 \\ sinx_1= \frac{-5+ \sqrt{193} }{12} \\ sinx_2 \neq \frac{-5- \sqrt{193} }{12} \\ \\ x_1=(-1)^{k}*arcsin( \frac{-5+ \sqrt{193} }{12})+ \pi k](https://tex.z-dn.net/?f=6cos%5E2x-5sinx%2B1%3D0+%5C%5C+6%281-sin%5E2x%29-5sinx%2B1%3D0+%5C%5C+6-6sin%5E2x-5sinx%2B1%3D0+%5C%5C+-6sin%5E2x-5sinx%2B7%3D0%28%2A-1%29+%5C%5C+6sin%5E2x%2B5sinx-7%3D0+%5C%5C+D%3D25%2B168%3D193+%5C%5C+sinx_1%3D+%5Cfrac%7B-5%2B+%5Csqrt%7B193%7D+%7D%7B12%7D+%5C%5C+sinx_2+%5Cneq+%5Cfrac%7B-5-+%5Csqrt%7B193%7D+%7D%7B12%7D+%5C%5C+%5C%5C+x_1%3D%28-1%29%5E%7Bk%7D%2Aarcsin%28+%5Cfrac%7B-5%2B+%5Csqrt%7B193%7D+%7D%7B12%7D%29%2B+%5Cpi+k+)
Второй корень не равен потому что область определения sinx [-1;1]
Объяснение:
n² + 6n + 9 = n² + 2 · 3 · n + 3² = (n + 3)²
При n ∈ N значение выражения (n + 3) будет ≥ 4. Тогда (n + 3)² будет ≥ 16.