(2^3)^100
вроде как то так, не помню)
4x + 12 + 10 = 6
4x + 22 = 6
4x = 6 - 22
4x = -12
x = -3
6 = 6
X=π/4+πn, n∈Z [5π;13π/2]= [5π; 6,5π]
n=0 x1=π/4+0π=π/4∉ [5π; 6,5π]
n=1 x2=π/4+π=5π/4∉ [5π; 6,5π]
n=2 x3=π/4+2π=9π/4∉ [5π; 6,5π]
n=3 x4=π/4+3π=13π/4∉ [5π; 6,5π]
n=4 x5=π/4+4π=17π/4∉ [5π; 6,5π]
<u>n=5 x6=π/4+5π=21π/4∈[5π; 6,5π]</u>
<u>n=6 x7=π/4+7π=25π/4∈ [5π; 6,5π]
</u>n=7 x8=π/4+8π=33π/4∉ [5π; 6,5π]
Ответ: 21π/4; 25π/4
436
tg1*tg5*tg9*.....*tg85*tg89=tg1*tg5*tg9*....*tg41*tg(90-41)*...*tg(90-5)*tg(90-1)=tg1*tg5*tg9*....*tg41*ctg41*...*ctg5*ctg1=1*1*...*1=1
437
a)(sinx/2+cosx/2)²=sin²x/2+2sinx/2*cosx/2+cos²x/2=1+sinx=0,4
sinx=0,4-1=-0,6
cosx=√1-sin²x=√1-0,36=√0,64=0,8
tgx=sinx/cosx=-0,6/0,8=-0,75
b)sinx/2+cosx/2=√(sinx/2+cosx/2)²=√(1+sinx)=√(1+0,21)=√1,21=1,1
(x^3 - 4x^2) -(3x-12) = 0;
x^2(x-4) - 3(x-4) = 0;
(x-4)(x^2 - 3) = 0;
x - 4 =0; ⇒ x1 = 4;
x^2 - 3 = 0; ⇒ x^2 = 3;⇒
x2 = sgrt3;
x3 = - sgrt3.
x1 * x3= - 4 sgrt3.