А) у3√4у2, где у> 0 б)7а √16/а2, где а< 0

1)  y^3 *  v  4y^2  =  y^3  *  2y  =  2y^4 2)  7a  *  v (  16  \  a^2)  =  7a  *  4  \  a  =  7a  *  4a^(-1)  =  28  a^  (  1  -  1)  =  28  a^0  =  28 

1. а) {x²+2x-3> 0     {2-x> 0 x²+2x-3> 0 f(x)=x²+2x-3 - парабола, ветви вверх. x²+2x-3=0 d=2² -4*(-3)=4+12=16 x₁= -2-4 = -3         2 x₂ = -2+4 =1             2         +                 -                   + -3 1 \\\\\\\\\\\\                         \\\\\\\\\\\\\\\ x∈(-∞; -3)  u  (1; +∞) 2-x> 0 -x> -2 x< 2 \\\\\\\\\\\\\\                     \\\\\\\\\\\\\\\\\\\\\\\\\\ -3 1 2 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x∈(-∞; -3) u (1; 2) б) {x²-3x-4≥0     {25-x²> 0 x²-3x-4≥0 f(x)=x²-3x-4 - парабола,ветви вверх. x²-3x-4=0 d=(-3)² - 4*(-4)=9+16=25 x₁= 3-5 = -1         2 x₂= 3+5 =4           2         +                 -                   + - -1 4 \\\\\\\\\\\\                       \\\\\\\\\\\\\\\\\\\\\ x∈(-∞; -1]u[4; +∞) 25-х²> 0 -x²+25> 0 f(x)=-x²+25 -x²+25=0 d=0 - 4*(-1)*25=100 x₁= 0-10 =-5         2 x₂ = 0+10 =5           2           -                       +               -                 -5 5                     \\\\\\\\\\\\\\\\\ x∈(-5; 5) \\\\\\\\\\\\\\\\\\\\\\\\                         \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ -5 -1 4 5                 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x∈(-5; -1] u [4; 5) в) {x+4> 1     {-x²-x+6> 0 x+4> 1 x> 1-4 x> -3 -3                       \\\\\\\\\\\\\\\\\\\\\\ -x²-x+6> 0 f(x)=-x²-x+6 - парабола, ветви вниз -x²-x+6=0 d=(-1)² -4*(-1)*6=1+24=25 x₁= 1 - 5 = 2         -2 x₂ = 1+5 = -3           -2       -                     +                     - -3 2                   \\\\\\\\\\\\\\\\ x∈(-3; 2)                   \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ -3 2                 \\\\\\\\\\\\\\\ х∈(-3; 2) г) {-x²+x+12≤0     {x²-7x> 0 -x²+x+12≤0 f(x)=-x²+x+12 - парабола, ветви вниз -x²+x+12 =0 x²-x-12=0 d=1²-4*(-12)=1+48=49 x₁= 1-7 = -3         2 x₂= 1+7 = 4         2         -                     +                     - -3 4 \\\\\\\\\\\\                           \\\\\\\\\\\\\\\\\\ x∈(-∞; -3] u [4; +∞) х² -7х> 0 f(x)=x²-7x - парабола, ветви вверх х²-7х=0 х(х-7)=0 х₁=0 х₂=7       +                 -                     + - 0 7 \\\\\\\\\\\                           \\\\\\\\\\\\\\\\\\\ х∈(-∞; 0) u (7; +∞) \\\\\\\\\\\\                                           \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ -3 0 4 7   \\\\\\\\\\\\\\\\\\\\\\\\                                                     \\\\\\\\\\\\\\\\\\\\\ x∈(-∞; -3] u (7; +∞)

Lgx=t t⁴-4t³+51t²-2t≥0 t*(t³-4t²+5t-2)≥0 t=0, t³-4t²+5t-2=0 t=0, t=1     1 -4 5 -2 1 1 -3 2   0 t³-4t²+5t-2=(t-1)*(t²-3t+2) t²-3t+2=0 t=1, t=2       +         -         -           + |||> t           1           0         2 t∈[-∞; 1]u[2; ∞] 1. lgx≤1 lgx≤lg10, 10> 1 знак неравенства не меняем {x> 0 x≤10 x∈(0; 10] 2. lgx≥2 lgx≥lg100 {x> 0 x≥100 x∈[100; ∞) ответ: х∈(0; 10]u[100; ∞)