Question

Giải PT
\(4\sqrt{x+1}=x^2-5x+14\)

Answer 1

Trả lời

x2−5x+14≐(x−3)2+x+5≥x+5≥x+1+4≥4x+1" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvea,arial,sans-serif; font-size:14px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">Ta có: \(x^2-5x+14=\left(x-3\right)^2+x+5\ge x+5\ge x+1+4\ge4\sqrt{x+1}\)x2−5x+14≐(x−3)2+x+5≥x+5≥x+1+4≥4x+1" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvea,arial,sans-serif; font-size:14px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">\(\Rightarrow VT\ge VP\)x2−5x+14≐(x−3)2+x+5≥x+5≥x+1+4≥4x+1" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvea,arial,sans-serif; font-size:14px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">Vậy để \(VT\ge VP\Leftrightarrow x=3\)(dấu "=" xảy ra)