Solve the following equation :
\(\dfrac{x+1}{49}+\dfrac{x+3}{47}=\dfrac{x+5}{45}+\dfrac{x+7}{43}\)
Solve the equation :
\(\dfrac{2x-1}{x-1}+1=\dfrac{1}{x-1}\)
Prove that for a, b is a positive number \(a^2-3ab^2+2b^2\) is also positive .
Considering the left and right sides :
\(\left(a^2-b^2\right)^2+\left(2ab\right)^2=\left(a^2+b^2\right)^2\)
Certificate as any posts after :
a , \(a^2+b^2\ge\dfrac{1}{2}\) với a + b = 1 .
b , \(a^2+b^2+c^2\ge\dfrac{1}{3}\) với a + b + c = 1
Polynomial Analysis into Factors :
\(x^4-6x^3+12x^2-14x+3\)
\(x^5+x^4+1\)