1.
a) B=∣x−2∣+31≤0+31=31.
Dấu '=' xảy ra khi x=2.
Vậy Bmax=31 khi x=2.
b) C=∣x∣x+2.
Nếu x>0 thì C=xx+2=1+x2 Cmax⇔xmin⇔x=1. ⇒Cmax=1+2=3.
Nếu x<0 thì C=−xx+2=−1−x2 Cmax⇔xmax⇔x=−1. ⇒Cmax=−1+2=1
Vậy Cmax=3 khi x=1.
2. M=x2+3∣y−2∣−1.
Ta có: x2≥0;∣y−2∣≥0∀x,y. ⇒x2+3∣y−2∣−1≥0+3.0−1=−1. ⇒M≥−1.
Dấu '=' xảy ra khi x=0;y=2.
Vậy Mmin=−1 khi x=0;y=2.
1.
a) B=∣x−2∣+31≤0+31=31.
Dấu '=' xảy ra khi x=2.
Vậy Bmax=31 khi x=2.
b) C=∣x∣x+2.
Nếu x>0 thì C=xx+2=1+x2 Cmax⇔xmin⇔x=1. ⇒Cmax=1+2=3.
Nếu x<0 thì C=−xx+2=−1−x2 Cmax⇔xmax⇔x=−1. ⇒Cmax=−1+2=1
Vậy Cmax=3 khi x=1.
2. M=x2+3∣y−2∣−1.
Ta có: x2≥0;∣y−2∣≥0∀x,y. ⇒x2+3∣y−2∣−1≥0+3.0−1=−1. ⇒M≥−1.
Dấu '=' xảy ra khi x=0;y=2.
Vậy Mmin=−1 khi x=0;y=2.