Question

cho x; y thỏa mãn điều kiện \(3\left(x\sqrt{y-9}+y\sqrt{x-9}\right)=xy\)

Tính giá trị biểu thức: \(S=\left(x-17\right)^{2018}+\left(y-19\right)^{2019}\)

Answer 1

Ta có:

\(VT=\sqrt{9x\left(xy-9x\right)}+\sqrt{9y\left(xy-9y\right)}\le\frac{9x+xy-9x}{2}+\frac{9y+xy-9y}{2}\)

\(=xy=VP\)

Dấu =  xảy ra khi \(x=y=18\)

\(\Rightarrow S=\left(18-17\right)^{2018}+\left(18-19\right)^{2019}=1-1=0\)

Answer 2

Ta có:

VT=\sqrt{9x\left(xy-9x\right)}+\sqrt{9y\left(xy-9y\right)}\le\frac{9x+xy-9x}{2}+\frac{9y+xy-9y}{2}VT=9x(xy−9x)​+9y(xy−9y)​≤29x+xy−9x​+29y+xy−9y​

=xy=VP=xy=VP

Dấu =  xảy ra khi x=y=18x=y=18

\Rightarrow S=\left(18-17\right)^{2018}+\left(18-19\right)^{2019}=1-1=0⇒S=(18−17)2018+(18−19)2019=1−1=0