Question

[Nguyễn trần Ngọc Bích]

1. x² - 4x +13 = 0  
2. Cho a,b > 0. CMR a+b \(\ge\) 2\(\sqrt{ab}\)
3. Áp dụng câu (2)CMR \(\frac{a^2}{b+c}\)+ \(\frac{b^2}{a+c}\)+ \(\frac{c^2}{a+b}\)\(\ge\)\(\frac{a+b+c}{2}\)
4. ( x² - \(\frac{25}{4}\))²  = 10x +1

Answer 1

[Võ Ngọc Trường An]

1. x²-4x+4+9=(x-4x+4)+9=(x-2)²+9 >=9. nên pt vô nghiệm

2. \(a+b\ge2\sqrt{ab}\Leftrightarrow\left(a+b\right)^2\ge4ab\Leftrightarrow a^2+2ab+b^2\ge4ab\)

\(\Leftrightarrow a^2-2ab+b^2\ge0\Leftrightarrow\left(a-b\right)^2\ge0\)( đúng). dpcm