1) 4х=24+х
4х-х=24
3х=24
х=24:3
х=8
2) 8х-8=20-6х
8х+6х=20+8
14х=28
х=28:14
х=2
3) 9-4х=3х-40
3х+4х=9+40
7х=49
х=49:7
х=7
4) 0,6х-5,4=-0,8х+5,8
0,6х+0,8х=5,8+5,4
1,4х=11,2
х=11,2:1,4
х=8
40·96+78x=6570
3840+78x=6570
78x=6570-3840
78x=2730
x=2730:78
x=35
Ответ: x=35.
Ширина 10 2/3см
Длина 10 2/3*1 7/8=32/3*15/8=20см
Высота 20*0,15=3см
Объем равен 10 2/3*20*3=32/3*60=32*20=640см²
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