S18 (сумма первых членов прогрессии) = (а1+а18)/2*18 a16 = a1 + 15d => 47=11+15d => 15d=36 => d=2,4 a18= a1 + 17d => 11 + 17*2,4 = 51,8 => S18= (11 + 51,8)/2*18 = 565,2
1-х,2-х+1.3-х+2,4-х+3
у=(х+х+1+х+2+х+3)/4=х+1,5
х=у-1,5
х+1=у-0,5
х+2=у+0,5
х+3=у+1,5
(y-1,5)(y-0,5)(y+0.5)(y+1,5)+1=(y²-0,25)(y²-2,25)+1=y^4-2,5y²+0,5625+1=
=y^4-2,5y²+1,5625=(y²-1,25)²
<span>log2(х-2)+log2x=3 здесь x=3,97
</span><span>log8x+log√2x=14 здесь x=e^28/3/4sqt3sqr2
</span>
<span>9^x-7*3^x-18=0 здесь x=2
</span>
<span>log3 1/27 здесь log(1)/27log(3)
</span>
<span>log√3x+log 3x=10 здесь x=e^20/3/3
</span>
4<span>x+2x-20=0</span> здесь x=10/3
B ₅- b₃=36 ;<span>
b</span>₇+b₅=240 .
<span>----------------
b</span>₁<span>- ?
q -?
</span>(b₄ -b₂) - ?
* * * * * * * * * * * * * *
{b₁q⁴ -b₁q² =36 ; b₁q⁶ +b₁q⁴ =240.⇔{b₁q²(q² -1)=12*3; b₁q⁴(q² +1) =12*20. ⇒
{ (q²-1) / q²(q² +1) =12*3/12*20 ; b₁ =36/ q²(q² -1) . * * * || q ≠0 ; q² ≠1|| * * *
----
(q² -1) / q²(q² +1) =3/20 обозн. t = q² >0.
(t - 1)/ t<span>(t +1) =3/20
</span>3t² -17t +20 =0 ⇒[ t=5/3 ; t =4.
<span>a)
</span>q² =5/3 ⇔ q =±√(5/3) и b₁ =36/ q²(q² -1) =36/(5/3)*(2/3) = 32,4.
b₄ -b₂ =b₁q³ -b₁q =b₁q(q² -1) =32,4.*( ±√(5/3) )* (5/3-1) =±7,2√15.
<span>----------
<span>b)
</span></span>q² =4 ⇔ q = ± 2 и b₁ =36/ 4(4-1) = 3.
b₄ -b₂ =b₁q(q² -1) =3*(±2)*3 = ± 18.
ответ :
<span>а</span>) b₁ = 32,4 ; q =±√(5/3) ; b₄ -b₂ = ±7,2√15 или
b) b₁ = 3 ; q = ± 2 ; b₄ -b₂ = ± 18 .