Find Minimum value of :

A = x² + 8x + 1

B = x² - x + 1

Find Maximum value of :

A = 2x - x²

B = 19 - 6x - 9x²

Prove that :

A = x² - xy + y² > 0 (\(\forall x,y\) ; \(A\ne0\))

Given rhombus ABCD , \(\widehat{C}=40^0\) , M is the midpoint of CD. Draw \(BH\perp AM\) at H .

Find the degree of \(\widehat{DBC};\widehat{AHD}\)

Given x, y \(\ge0\) satisfy x³ + y³ = x - y

Find maximum of A know A = x² + y²

With a,b \(\in Z\) . Show that : If 4a² + 3ab - 11b² \(⋮5\) so that a⁴ - b⁴ \(⋮5\)

Given x = ax + by ; y = ax + cz ; z = by + cz    and    \(x+y+z\ne0\)

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

Given triangle ABC right at A, AH is height . Draw \(HD\perp AB\) at D, \(HE\perp AC\) at E

Prove that : AH² = BH.HC

                    AB² = BH.BC 

Given square ABCD. O is the intersection of AC and BD, M \(\in\) OB . Draw \(ME\perp AB\) at E , \(MF\perp BC\) at F.

a) Which special quadrilateral that the quadrilateral BEMP does ? Why ?

b) Prove that : AC // EF

Given triangle ABC Isosceles at A. On AB , choose D , through D draw a ray parallel with BC and cut AC at E.

a) Where D is located on AB so that BD = DE = EC ?

Given abc = 1 

Prove that : \(M=\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+a}+\dfrac{c}{ca+c+1}=1\)

Given a,b,c > 0

Prove that : \(\dfrac{ab}{c}+\dfrac{bc}{a}+\dfrac{ca}{b}\ge a+b+c\)

Solve the inequation :

\(\dfrac{4x-3}{x-1}< 5\)

Solve the inequation :

\(\dfrac{x+5}{2006}+\dfrac{x+4}{2007}+\dfrac{x+3}{2008}< \dfrac{x+9}{2002}+\dfrac{x+1}{2010}+\dfrac{x+11}{2000}\)

Solve the equation by using inequality :

\(2.\left(\dfrac{x^{10}}{y^2}+\dfrac{y^{10}}{x^2}\right)+x^{16}+y^{16}=4\left(1+x^2y^2\right)-10\)

Solve the equation : 

x⁴ = 4x + 1 

Solve the equation :

\(\dfrac{x}{\left(a-b\right)\left(a-c\right)}+\dfrac{x}{\left(b-a\right)\left(b-c\right)}+\dfrac{x}{\left(c-a\right)\left(c-b\right)}=2\) with \(a\ne b\ne c\)

Find the edges of polygons with the sum of angles equals to 1260

Each angles of equilateral polygon n edges equals 144⁰ . Find n

Given quadrilateral ABCD with \(\widehat{A}=70^0\) , two ray bisector inside of \(\widehat{B}\)  and \(\widehat{C}\) cut at I , two ray bisector outside of \(\widehat{B}\) and \(\widehat{C}\) cut at H.

Prove that : All angles in quadrilteral BICH does not depend on magnitude of B and C.