А) [a*b^(1/2) / (a^(1/2) + b^(1/2)) + b*a^(1/2) / (a^(1/2) - b^(1/2))]*a^(-1/2)*b^(-1/2) =
= [a*b^(1/2)*(a^(1/2)-b^(1/2)) + b*a^(1/2)*(a^(1/2)+b^(1/2))]/(a - b)*a^(-1/2)*b^(-1/2) =
= a^(1/2)*b^(1/2)*[a^(1/2)*(a^(1/2)-b^(1/2)) + b^(1/2)*(a^(1/2)+b^(1/2))] /
/ (a - b)*a^(-1/2)*b^(-1/2) =
= [a^(1/2)*(a^(1/2)-b^(1/2)) + b^(1/2)*(a^(1/2)+b^(1/2))] / (a - b) =
= (a - a^(1/2)*b^(1/2) + a^(1/2)*b^(1/2) + b) / (a - b) = (a + b)/(a - b)
б) 1/a^(-1/4) = a^(1/4), поэтому
[(a^(1/4) - b^(1/4))^2 + 1 / (a^(1/4) + b^(1/4))^2] : [(a^(1/2) + b^(1/2)) / (a - b)] =
= [(a^(1/4) - b^(1/4))^2*(a^(1/4) + b^(1/4))^2 + 1] / (a^(1/4) + b^(1/4))^2 :
: (a^(1/2) + b^(1/2)) / [(a^(1/2) + b^(1/2))*(a^(1/2) - b^(1/2))] =
= [(a^(1/2) - b^(1/2))^2 + 1] / (a^(1/4) + b^(1/4))^2 : 1 / (a^(1/2) - b^(1/2)) =
= [(a^(1/2) - b^(1/2))^2 + 1] / (a^(1/4) + b^(1/4))^2 * (a^(1/2) - b^(1/2))
Больше не сокращается, наверное, какая-то ошибка в задании
3/5 = 0,6
4/5 = 0,8
0,8-0,6 = 0,2
Ответ : на 0,2 км
или можно записать как 1/5км
L=2πr
r=l/2π
r1=56/(2*3.14)=8.9cm
r2=7/(2*3.14)=1.12m
r3=18/(2*3.14)=2.87m
1) 3^x-3^(x+3)=-78
3^x-3^x*3^3=-78
3^x(1-27)=-78
3^x*(-26)=-78
3^x=3
x=1
ответ: x=1
2)2^(2x)-6*2^x+8=0
2^x=t
t²-6t+8=0
D/4=9-8=1
t1=(3+1)/1=4
t2=(3-1)/1=2
2^x=2², x1=2
2^x=2, x2=1
Ответ: х1=2, х2=1
3) 3*9^x-10*3^x+3=0
3^x=t
3t²-10t+3=0
D/4=25-9=16
t1=(5+4)/3=3
t2=(5-4)/3=1/3
3^x=3, x1=1
3^x=1/3, x2=-1
ответ: х1=1
х2=-1
4) 4*(1/16)^x-17*(1/4)^x+4=0
(1/4)^x=t
4*t²-17*t+4=0
D=289-64=225
t1=(17+15)/8=4
t2=(17-15)/8=1/4
(1/4)^x=4, x1=-1
(1/4)^x=1/4
x2=1
ответ: х1=-1, х2=1
