1/11xy . căn121x^2/y^6 với x<0,y>0
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\(Q=7x^2y-2xy+\dfrac{1}{2}x^2y-xy+11xy-\dfrac{1}{3}x+\dfrac{1}{3}+\dfrac{2}{3}x-\dfrac{1}{6}\)
\(Q=\dfrac{15}{2}x^2y+8xy-x-\dfrac{1}{6}\)
Q = ( 7x\(^2\)y + \(\dfrac{1}{2}\)x\(^2\)y ) + ( -2xy - xy + 11xy ) +( -\(\dfrac{1}{3}\)x + \(\dfrac{2}{3}\)x ) + ( -\(\dfrac{1}{3}\) - \(\dfrac{1}{6}\) )
= \(\dfrac{15}{2}\)x\(^2\)y + 8xy + \(\dfrac{1}{3}\)x _ \(\dfrac{1}{2}\)
\(\frac{1}{11xy}\sqrt{\frac{121x^2}{y^6}}=\frac{1}{11xy}.\frac{11x}{y^3}=\frac{1}{y^4}\)
4/11 x y - 6/11 = 2/5
4/11 x y = 2/5+6/11
4/11 x y = 52/55
y = 52/55 : 4/11
y = 13/5
4/11xy-6/11=2/5
=>4/11xy=2/5+6/11
=>4/11xy=52/55
=>y=52/55:4/11
=>y=13/5
\(\left(x-2\right)^4+\left(2y-1\right)^{2022}< =0\)
mà \(\left(x-2\right)^4+\left(2y-1\right)^{2022}>=0\forall x,y\)
nên \(\left\{{}\begin{matrix}x-2=0\\2y-1=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=\dfrac{1}{2}\end{matrix}\right.\)
\(M=11xy^2+4xy^2=15xy^2=15\cdot2\cdot\left(\dfrac{1}{2}\right)^2=\dfrac{15}{2}\)