XD moi x
\(yx^2+y=x^2+3x+5\Leftrightarrow\left(y-1\right)x^2-3x+\left(y-5\right)=0\)
dat y-1=a cho gon
\(ax^2-3x+\left(a-4\right)=0\)(1)
tim DK a de phuong trinh tren(1) co nghiem
a=0=>-3x-4=0=> x=4/3
voi a \(\ne0\)(1) phuong trinh bac 2
=>delta(x)=3^2-4a.(a-4)\(\ge0\)
\(\Leftrightarrow9-4a^2+16a\ge0\Leftrightarrow4a^2-16a-9\le0\)
delta"(a)=4^2-4.(-9)=16+36=52=4.13
\(\orbr{\begin{cases}a_1=\frac{4-2\sqrt{13}}{4}=1-\frac{\sqrt{13}}{2}\\a_2=\frac{4+2\sqrt{13}}{4}=1+\frac{\sqrt{13}}{2}\end{cases}}\)
\(\left(1-\frac{\sqrt{13}}{2}\right)\le a\le1+\frac{\sqrt{13}}{2}\)
\(1-\frac{\sqrt{13}}{2}\le y-1\le1+\frac{\sqrt{13}}{2}\)
\(2-\frac{\sqrt{13}}{2}\le y\le2+\frac{\sqrt{13}}{2}\)
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