Give x⁴+y⁴+z⁴=3.Find the minium value of P=x²(x+y)+y²(y+z)+z²(z+x)

Solve the equation:\(x^2+\left(\dfrac{x}{x+1}\right)^2=1\)

Givea>b>c>0 and a²+b²+c²=1.Prove that:\(\dfrac{a^3}{b+c}+\dfrac{b^3}{c+a}+\dfrac{c^3}{a+b}\ge\dfrac{1}{2}\)

Give a,b,c>0.Prove that:\(\dfrac{a^2}{b^2+c^2}+\dfrac{b^2}{c^2+a^2}+\dfrac{c^2}{a^2+b^2}\ge\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\)

Solve the equation:

2011^x=x²⁰¹¹

Find the number of roots of the following equation

(x-2017)(x²-2018²)(x³-2019³)(x⁴-2020⁴)=0

Let P=|x²-5|+|x²-6|+|x²-2017|.What is the value of x so that P attains its minimum value?

Let x be an integer.Find the maximum value of the expression M=\(\dfrac{2017}{2x^2-2x+1}\)

Find the next number to fill in dots:

1,3,7,15,31,.............

How many numbers between 138 and 752?