Có 25t\(^2\) - 260t + 1700
= ( 5t )\(^2\) - 2 . 5t . 26 + 26\(^2\) + 1024
= ( 5t - 26 ) \(^2\) + 1024
\(\Rightarrow\) x\(^2\) = ( 5t - 26 ) \(^2\) + 1024
Có ( 5t - 26 )\(^2\) \(\ge\) 0 với mọi t
\(\Rightarrow\) ( 5t - 26 ) \(^2\) + 1024 \(\ge\) 1024 với mọi t
Dấu " = " xảy ra \(\Leftrightarrow\) ( 5t - 26 )\(^2\) = 0
\(\Rightarrow\) t = \(\frac{26}{5}\)
Vậy x\(^2\) đạt GTNN là 1024 khi t = \(\frac{26}{5}\)
\(x^2=25t^2-260t+1700\)
\(x^2=\left(5t\right)^2-2\cdot5t\cdot26+26^2+1024\)
\(x^2=\left(5t-26\right)^2+1024\)
Vì \(\left(5t-26\right)^2\ge0\forall t\)
\(\Rightarrow x^2\ge1024\forall t\)
Dấu "=" xảy ra \(\Leftrightarrow5t-26=0\Leftrightarrow t=\frac{26}{5}\)
Vậy x2min = 1024 <=> t = 26/5
