(5^x-3*3^x)/(3*5^x-5*3^x)-3^x/5*x≥0
(5^2x-3*x*5^x-3*5^x*3^x+5*3^2x)/(3*5^2x-5*3^x*5*x)≥0
разделим чмслитель и знаменатель на 3^2x
((5/3)^x-6*(5/3)^x+5)/(3*(5/3)^2x-5*(5/3)^x)≥0
(5/3)^x=a
(a²-6a+5)/(3a²-5a)≥0
a²-6a+5=0
a1+a2=6 U a1*a2=5
a1=1 U a2=5
3a²-5a=0
a(3a-5)=0
a=0 a=5/3
+ _ + _ +
----------------(0)--------------[1]-------------(5/3)-----------------[5]-----------------
a<0⇒(5/3)^x<0 нет решения
1≤a<5/3⇒1≤(5/3)^x<5/3⇒0≤x<1
a>5⇒(5/3)^x>5⇒x>log(5/3)5
x∈[0;1) U (log(5/3)5;∞)
4y^3 - y =0
y(4y^2 - 1) = 0
y =0
4y^2 - 1 = 0
4y^2 = 1
y^2 = 1/4
y = 1/2
y = - 1/2
Ответ: y1 = 0, y2 = 1/2, y3 = - 1/2.
x^4 - x^2 = 0
x^2(x^2 - 1)=0
x^2 = 0
x = 0
x^2 - 1 = 0
x^2 = 1
x = 1
x = - 1
Ответ: x1 = 0, x2 = 1, x3 = - 1
9y^2 - 4y^4 = 0
y^2( 9 - 4y^2) = 0
y^2 = 0
y = 0
9 - 4y^2 = 0
- 4y^2 = - 9
4y^2 = 9
y^2 = 9/4
y = 3/2
y =- 3/2
Ответ: y 1 = 0, y2 = 3/2, y3 = - 3/2.