` P = x^2 +3x +5 = x^2 + 2.3/2 x + 5 = (x^2 +2. 3/2x + 9/4) +11/4 `
` =( x + 3/2)^2 +11/4 \ge 11/4`
Vậy GTNN ` P = 11/4` khi ` x+3/2 = 0 \to x = -3/2`
`Q = 3/2 x^2 + x +1 = 3/2 (x^2 + 2/3 x) +1 = 3/2 ( x^2 + 2. 1/3 x + 1/9) +5/6`
` = 3/2 ( x +1/3)^2 +5/6 \ge 5/6`
Vậy GTNN ` P = 5/6` khi ` x +1/3 = 0 \to x = -1/3`
` R = x^2 +2y^2 + 2xy - 2y`
` = (x^2 +2xy +y^2 ) +(y^2 -2y+1) -1`
` = (x+y)^2 + (y-1)^2 -1 \ge -1`
Vậy GTNN ` R = -1` khi
$ \begin{cases} x+y=0\\\\\\ y-1 = 0\end{cases}\\$
$ \leftrightarrow \begin{cases} x =-1 \\\\\\ y=1\end{cases}\\$
` T = (x+1)(x+2)(x+3)(x+4) = [ (x+1)(x+4)].[(x+2)(x+3)]`
` = (x^2+5x+4)(x^2+5x+6)`
Đặt ` x^2 +5x +5 = t`
`\to T = ( t-1)(t+1) = t^2 -1 \ge -1`
Vậy GTNN ` T = -1` khi ` t^2 = 0 \to t = 0 `
`\to x^2 +5x +5 = 0 \to (x^2 +5x + 25/4) - 5/4=0`
`\to (x+5/2)^2 = 5/4`
`\to` \(\left[ \begin{array}{l}x+\dfrac{5}{2}= \dfrac{\sqrt{5}}{4}\\\\x+\dfrac{5}{2}= \dfrac{-\sqrt{5}}{4}\end{array} \right.\)
`\to` \(\left[ \begin{array}{l}x= \dfrac{\sqrt{5}-5}{2} \\\\x= \dfrac{-\sqrt{5}-5}{2}\end{array} \right.\)
