With x,y,z \(\in R^+\) that satisfies \(x\ge z\).
Show that: \(\dfrac{xz}{y^2+yz}+\dfrac{yz}{xz+yz}+\dfrac{x+2z}{x+z}\ge\dfrac{5}{2}\)
With a,b,c are three non-negative numbers that satisfy a + b + c = 3
Show that: \(\Sigma\left(a\sqrt{a+8}+2\right)\ge15\)
Let a,b,c > 0 that satify a + b + c = 1
Find minimum value of \(P=\dfrac{a}{a^2+1}+\dfrac{b}{b^2+1}+\dfrac{c}{c^2+1}+\dfrac{1}{9abc}\)
Let a,b,c are positive real numbers satisfy \(a^2+b^2+c^2=1\)
Show that : \(\Sigma\dfrac{a^3}{b+c}\ge\dfrac{1}{2}\)
Let P is an integer number , show that :
\(GCD\left(P^2-1;P^2+1\right)\ne1\)
Give a2 + b2 = c2 + d2 = 2017 and ac + bd = 0
Calculate the value of A = ab + cd
Find the triple pairs of integer (x;y;z) that satisfy:
\(2^x+2^y+2^z=2336\)
Give an equilateral hexagon. Six birds land on six tops. After a few minutes, six bird fly away and land on 6 tops again. (They don's have to land on the top that they have landed). Show that , there are exist at least three birds that the triangle they have made before fly equals to the triangle they have made after land.
Suppose p is an odd prime number and \(m=\dfrac{9p-1}{8}\)
Prove that : m is an odd integer not divisible by 3 and
\(3^{m-1}\equiv1\) (mod m)
With a,b,c are three lengths of three edges of a triangle.
Show that : \(A=\dfrac{a}{b+c-a}+\dfrac{b}{c+a-b}+\dfrac{c}{a+b-c}\ge3\)
Show that : with x,y are positive interger numbers then \(x⋮̸xy-1\)
Find all the pairs of real numbers (x;y;z) satisfy
\(x=\dfrac{4z^2}{1+4z^2}\) ; \(y=\dfrac{4x^2}{1+4x^2}\) ; \(z=\dfrac{4y^2}{1+4y^2}\)
Show that : The final digit of the numbers are in the form of n and n5 are in the same
Show that :
An odd number p = 10s + r (with r equals to 1 ; 3 ; 7 or 9) divisible by a natural number T = 10x + a when and only when (x - ka) \(⋮\) p , k is a number satisfy for 10k + 1 \(⋮\) p .
Find all integer value of a,b,c satisfy \(a^2+b^2+c^2=a^2.b^2\)
Find value of (a;b;c) are integers so that \(a^2+b^3=c^4\) (Condition : \(a,b,c\ge0\))
Find all integer value of x,y know : \(y^2=x\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
How to determine a prime number ? Please help me :< !
Find x for A's value has maximum
A = \(\dfrac{x^2-2x+2016}{x^2}\) (With x > 0)
Given x,y are two positive real numbers (x,y differ to 0) satisfy \(5x^2+\dfrac{y^2}{4}+\dfrac{1}{4x^2}=\dfrac{5}{2}\)
Find minimum and maximum value of expression \(A=2013-xy\)
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