5)ОДЗ {х>0
{4-3х>0;-3х>-4;х<4/3
0<х<4/3
1)х=(4-3х)⁴
((4-3х)²)²-(х¹/²)²=0
((4-3х)²+х¹/²)((4-3х)²-х¹/²)=0
1)(4-3х)²+х¹/²=0
16-24х+9х²+х¹/²=0
16-24(х¹/²)²+9*(х¹/²)⁴+х¹/²=0
х¹/²=а>0
16-24а²+9а⁴+а=0
9а⁴-9а²-15а²+а+16=0
9а²(а²-1)-15(а+1)(а-16/15)=0
3(а+1)(3а²(а-1)-5(а-16/15)=0
1)а=-1 не подходит
2)3а³-3а²-5а+16/3=0
9а³-9а²-15а+16=0
13x-14-3x²=0
-3x²+13x-14=0
3x²-13x+14=0
D=169-4*3*14=1
x₁=(13+1)/6=7/3=2 1/3
x₂=(13-1)/6=2