Given x,y,z > 0 satisfy \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}\ge2\) . Prove that : xyz \(\le\) \(\dfrac{1}{8}\)

Find all square numbers writein by 4 digits know if we add into thousands 1 unit , add into hundreds 3 units, add into tenth 5 unit and into unit row 3 unit so that we still have a square number. 

Find the surplus in division expression :

(x + 1)(x + 3)(x + 5)(x + 7) + 2013  /   x² + 8x + 12

Solve the equation :

\(x+\dfrac{2a\left|x+a\right|}{x}=\dfrac{a^2}{x}\) 

Solve the equation :

a) (x - 3)³ - (x - 3)(x² + 3x + 9) + 6(x + 1)² = 15

b) x(x - 5)(x + 5) - (x + 2)(x² - 2x + 4) = 3

This web is too boring, the coordinator's question written by word, all the thread are by word. This is Math You Like ..... not Liter-Math You Like. So, try too fix it ...... if don't .... students in this page don't like to come here and play. 

Given triangle ABC with angle A = 90⁰ , find the value of two angle B and C know triangle ABC is the isosceles triangle

Prove Bunyakovsky inequality :

With 2 sets of numbers : \(\left(a_1;a_2;......;a_n\right);\left(b_1;b_2;......;b_n\right)\) so that :

\(\left(a_1^2+a_2^2+......+a_n^2\right).\left(b_1^2+b_2^2+.......+b_n^2\right)\ge\left(a_1.b_1+a_2.b_2+......+a_n.b_n\right)^2\)

Prove that :

A = 1 + 2 + 2² + 2³ + .......... + 2¹⁴ \(⋮\) 31

Prove that :  In a quadrilateral, the sum of four angles is 360

Use the sum of three angles in triangle to prove it.

A boat can hold three people, one of whom needs to row to cross a river that is 20 yards wide. What is the maximum distance the boat must travel to transport 9 people from the left bank of the river to the right bank ? 

P/s: There must be at least 2 people on boat to run it  :) 

Give a² + b² + c² = 2p

Prove that : (p - a)² + (p - b)² + (p - c)² = a² + b² + c² 

Calculate :

\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.3}+.....+\dfrac{1}{a+\left(a+1\right)+\left(a+2\right)}\)

Give a,b,c > 0 

Prove that : \(1< \dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< 2\)

Give a,b,c,d > 0 

Prove that : \(1< \dfrac{a}{a+b+c}+\dfrac{b}{b+c+d}+\dfrac{c}{c+d+a}+\dfrac{d}{d+a+b}< 2\)

1. Find x know :

a) x⁴ - x³ + x² - x = 0

b) x² - 8² = 0

c) (x + 1) + (x + 2) + (x + 3) + ...... + (x + 10) = 55

Give square triangle ABC at A. Draw AH perpendicular BC at H. Draw HD, HE are high lines of AB and AC.

a) Prove that : AH = DE

b) Call I is the midpoint of HB, K is the midpoint of HC. Prove that : DI // EK 

Good luck :) 

With a + b + c = \(\dfrac{3}{2}\).

Prove that: \(a^2+b^2+c^2\ge\dfrac{3}{4}\)

Prove that with every integer n so :

\(\dfrac{n^3}{3}+\dfrac{n^3}{2}+\dfrac{n^3}{6}\) is integer number .

Next :)

Given triangle ABC , draw outside triangle two squares ABDE and ACFH

a) Prove that : EC = BH ; EC \(\perp\) BH

b) Call M,N are center of  squares ABDE, ACFH. Call I is the midpoint of BC. Which triangle MIN is ? Why ?