Question

Tìm GTNN của :

a) A=5/4x^2+xy+y^2-3x+5

b) B=x^2+5y^2+4xy+6y+6x-12

 

Answer 1

Giúp mik cần gấp mai thầy ktra r!!!

Answer 2

\(a.A=\left(x^{^2}+2xy+y^{^2}\right)+\left(\dfrac{1}{4}x^{^2}-3x+9\right)-4\\ =\left(x+y\right)^{^2}+\left(\dfrac{1}{2}x-3\right)-4\)

gtnn khi dấu ''='' xảy ra ⇔x=6 và y=-6

 

Answer 3

b) \(B=x^2+5y^2+4xy+6x+6y-12\)

\(< =>\left(x+2y\right)^2+y^2+6\left(x+y\right)-12\)

\(< =>\left(x+2y\right)^2+6\left(x+2y\right)+y^2-6y-12\)

\(< =>\left(x+2y\right)^2+6\left(x+2y\right)+9+y^2=6y+9-30\)

\(< =>\left(x+2y+9\right)^2+\left(y-3\right)^2-30\)

Vay GTNN cua B=-30<=>x=-15,y=3

a) A=\(\dfrac{5}{4}x^2+xy+y^2-3x+5< =>\left(x+y\right)^2+\left(\dfrac{1}{2}x-3\right)^2-4\)

Vay GTNN cua A=-4 <=>x=6 ,y=-6