Question

1, tìm x, y biết 

a) x² + x +1/4 = 4x²

b) 2x² + 2xy + y² - 2x +1 = 0

2, cM 3x² + 6x +100 >0 

3, tìm GTNN của biểu thức : 9x² + 3x -2 

help meee !!!!!!!

ai nhanh mik tik cho :3

Answer 1

a)

\(x^2+x+\frac{1}{4}=4x^2\)

\(x^2+2\cdot x\cdot\frac{1}{2}+\left(\frac{1}{2}\right)^2=\left(2x\right)^2\)

\(\left(x+\frac{1}{2}\right)^2=\left(2x\right)^2\)

\(\Leftrightarrow x+\frac{1}{2}=2x\)

\(\Leftrightarrow x=\frac{1}{2}\)

Answer 2

2)

\(3x^2+6x+100\)

\(=3\left(x^2+2x+\frac{100}{3}\right)\)

\(=3\left(x^2+2\cdot x\cdot1+1^2+\frac{100}{3}\right)\)

\(=3\left[\left(x+1\right)^2+\frac{100}{3}\right]\)

\(=3\left(x+1\right)^2+100\ge100\forall x\left(đpcm\right)\)