Question

Giải câu b,d nhé

Answer 1

b.

\(x^2+2y^2+2xy-2x+2=0\)

\(\Leftrightarrow2x^2+4y^2+4xy-4x+4=0\)

\(\Leftrightarrow\left(x^2+4xy+4y^2\right)+\left(x^2-4x+4\right)=0\)

\(\Leftrightarrow\left(x+2y\right)^2+\left(x-2\right)^2=0\)

Do \(\left\{{}\begin{matrix}\left(x+2y\right)^2\ge0\\\left(x-2\right)^2\ge0\end{matrix}\right.\) ;\(\forall x;y\)

\(\Rightarrow\left(x+2y\right)^2+\left(x-2\right)^2\ge0\)

Dấu "=" xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}x+2y=0\\x-2=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=-1\end{matrix}\right.\)

Answer 2

câu b nè hong biết đúng hong 

Answer 3

d.

\(9x^2+29y^2=5\left(4y-6xy-5\right)\)

\(\Leftrightarrow9x^2+29y^2-20y+30xy+25=0\)

\(\Leftrightarrow\left(9x^2+30xy+25y^2\right)+\left(4y^2-20y+25\right)=0\)

\(\Leftrightarrow\left(3x+5y\right)^2+\left(2y-5\right)^2=0\)

Do \(\left\{{}\begin{matrix}\left(3x+5y\right)^2\ge0\\\left(2y-5\right)^2\ge0\end{matrix}\right.\) ;\(\forall x;y\)

\(\Rightarrow\left(3x+5y\right)^2+\left(2y-5\right)^2\ge0\)

Dấu "=" xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}3x+5y=0\\2y-5=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{25}{6}\\y=\dfrac{5}{2}\end{matrix}\right.\)