Find positive integer x,y know:

a. 5^x - 17^y = 2^xy and x-y=5; 2x + 3^y = xy

b. x + 2y – 3z = 5^xyz và (x – 2y)(y + 7) – x = 19² .( xyz > 0)

Please help me

Let the triangle ABC and M be a point lying on the BC edge. Via point A straight line xy parallel BC. Through point M straight line parallel to AB, AC intersect the line xy in D and E respectively.

a, Prove that AD = BM and \(\Delta EMD=\Delta CAB\)

b, Prove that three lines AM, BD, EC concurrent

Find all integer number x,y satify: \(\dfrac{2017^x-2016^{y+1}}{2015}\) is a square number

Please do fast, I need it before this morning

Given: \(\left\{{}\begin{matrix}x,y>0\\x+y=1\end{matrix}\right.\)

Find the Minimum of \(A=\dfrac{1}{x^2}+\dfrac{1}{y^2}\)

Find the surplus when divide (n³ - 1)¹¹¹ . (n² - 1)³³³  for n.

Shorten the following expression:

\(A=\dfrac{x\left|x-2\right|}{x^2+8x-20}+12x-3\)

Given x = 2005

Calculator:

\(B=x^{2005}-2006x^{2004}+2006x^{2003}-2006x^{2002}+...+2006x-1\)

Find 3 positive integer number a,b,c , know:

\(\left\{{}\begin{matrix}a^3+3a^2+5=5^b\\a+3=5^c\end{matrix}\right.\)

Given x,y,z are positive numbers.

Prove that:

\(\dfrac{x}{2x+y+z}+\dfrac{y}{2y+x+z}+\dfrac{z}{2z+x+y}\le\dfrac{3}{4}\)

Find max of \(A=\dfrac{3-4x}{x^2+1}\)

Given: \(x^2+x+1=0\)

Calculator: \(A=x+\dfrac{1}{x}\)

Prove that:

\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)

Prove that:

\(\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{25}+...+\dfrac{1}{n^2+\left(n+1\right)^2}< \dfrac{1}{2}\)

Given: \(\dfrac{x}{y+z+1}=\dfrac{y}{x+z+2}=\dfrac{z}{x+y-3}=x+y+z\)

Calculate: \(A=\dfrac{x^2+y^2+z^2}{x^2-y^2-z^2}\)

Prove that:

\(\left\{{}\begin{matrix}\left|x+y\right|\le\left|x\right|+\left|y\right|\\\left|x-y\right|\ge\left|x\right|-\left|y\right|\end{matrix}\right.\)

Given: \(\left\{{}\begin{matrix}a+b+c=a^2+b^2+c^2=1\\x:y:z=a:b:c\end{matrix}\right.\)

Prove that: \(\dfrac{\left(x+y+z\right)^2}{x^2+y^2+z^2}=1\)

Given this picture. Prove that: M is midpoint of DE

Given serial number:

a, 3     ;      24      ;     63      ;     120      ;     195    ;     ......

b, 20   ;      64      ;    132     ;     224     ;      340    ;    ......

What is 100^th number of each serial? What is each rule.

Given equation:

\(f\left(x\right)=ax^2+bx+c\)

Prove that:

\(f\left(-2\right)\cdot f\left(3\right)\le0\) know:

\(13a+b+2c=0\)

Help me fast!