Question

cho đa thức:\(A=x^2-14x+50\) chứng tỏ A>0 với mọi X

Answer 1

\(A=x^2-14x+50=\left(x^2-14x+49\right)+1=\left(x-7\right)^2+1\ge1>0\forall x\)

Answer 2

\(=(x^2-2.7.x+7^2)+1\)

\(=(x-7)^2+1\)

\(Vì (x-7)^2\)\(\ge\)0\(\forall\)\(x\) \(\Rightarrow\)\((x-7)^2+1\)\(\ge\)\(1\)\(\forall\)\(x\)

\(hay x^2-14x+50 >0\)\(\forall\)\(x\)

Answer 3

\(A=x^2-14x+50=\left(x^2-14x+49\right)+1=\left(x-7\right)^2+1\ge1>0\forall x\)