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a: \(\left\{{}\begin{matrix}x_1+x_2=8\\x_1x_2=6\end{matrix}\right.\)
\(D=x_1^4-x_2^4=\left(x_1+x_2\right)\left(x_1-x_2\right)\left(x_1^2+x_2^2\right)\)
\(=8\cdot\left[\left(x_1+x_2\right)^2-2x_1x_2\right]\cdot\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}\)
\(=8\cdot\left[8^2-2\cdot6\right]\cdot\sqrt{8^2-4\cdot6}\)
\(=8\cdot52\cdot2\sqrt{10}=832\sqrt{10}\)
b: \(E=\left(x_1^2+x_2^2\right)^2-2x_1^2\cdot x_2^2\)
\(=52^2-2\cdot\left(x_1\cdot x_2\right)^2=52^2-2\cdot6^2=2632\)
c: \(F=\dfrac{3x_2^2+3x_1^2}{\left(x_1\cdot x_2\right)^2}=\dfrac{3\cdot52}{6^2}=\dfrac{13}{3}\)
x1+x2=3; x1x2=-7
\(B=\left|x_1-x_2\right|=\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}\)
\(=\sqrt{3^2-4\cdot\left(-7\right)}=\sqrt{37}\)
\(F=\left(x_1^2+x_2^2\right)^2-2\left(x_1\cdot x_2\right)^2\)
\(=\left[3^2-2\cdot\left(-7\right)\right]^2-2\cdot\left(-7\right)^2\)
\(=23^2-2\cdot49=431\)
\(x^2-3x+2=0\)
\(\Leftrightarrow x^2-x-2x+2=0\)
\(\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_1=2\\x_2=1\end{matrix}\right.\)
\(C=x_1-x_2=2-1=1\)
Vậy \(C=1\)
Đặt f(x)=0
=>\(x^2-3x-5=0\)
=>\(x^2-3x+\frac94-\frac{29}{4}=0\)
=>\(\left(x-\frac32\right)^2=\frac{29}{4}\)
=>\(\left[\begin{array}{l}x-\frac32=\frac{\sqrt{29}}{2}\\ x-\frac32=-\frac{\sqrt{29}}{2}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac{\sqrt{29}+3}{2}\\ x=\frac{-\sqrt{29}+3}{2}\end{array}\right.\)
\(g\left(\frac{\sqrt{29}+3}{2}\right)=\left(\frac{3+\sqrt{29}}{2}\right)^2-4=\frac{\left(3+\sqrt{29}\right)^2-16}{4}\)
\(=\frac{9+29+6\sqrt{29}-16}{4}=\frac{22+6\sqrt{29}}{4}=\frac{11+3\sqrt{29}}{2}\)
\(g\left(\frac{-\sqrt{29}+3}{2}\right)=\left(\frac{-\sqrt{29}+3}{2}\right)^2-4\)
\(=\frac{29+9-6\sqrt{29}}{4}-4=\frac{38-6\sqrt{29}-16}{4}=\frac{22-6\sqrt{29}}{4}=\frac{11-3\sqrt{29}}{2}\)
\(g\left(x_1\right)\cdot g\left(x_2\right)\)
\(=\frac{11+3\sqrt{29}}{2}\cdot\frac{11-3\sqrt{29}}{2}=\frac{121-9\cdot29}{4}=\frac{-140}{4}=-35\)