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Ta có:
\(\dfrac{a}{b}=ab\Rightarrow a=\dfrac{a}{b^2}\Rightarrow b^2=1\Rightarrow\left[{}\begin{matrix}b=1\\b=-1\end{matrix}\right.\)
+) Nếu b=1 \(\Rightarrow ab=a+b\Rightarrow a=a+1\left(vôlí\right)\)
+) Nếu \(b=-1\Rightarrow ab=a+b\Rightarrow-a=a-1\Rightarrow a=\dfrac{1}{2}\)
\(T=a^2+b^2=\left(\dfrac{1}{2}\right)^2+\left(-1\right)^2=\dfrac{1}{4}+1=\dfrac{5}{4}\)
ab=ab⇒a=ab2⇒b2=1⇒[b=1b=−1ab=ab⇒a=ab2⇒b2=1⇒[b=1b=−1
+) Nếu b=1 ⇒ab=a+b⇒a=a+1(vôlí)⇒ab=a+b⇒a=a+1(vôlí)
+) Nếu b=−1⇒ab=a+b⇒−a=a−1⇒a=12b=−1⇒ab=a+b⇒−a=a−1⇒a=12
T=a2+b2=(12)2+(−1)2=14+1=54
a : b = ab
=> a = ab.b = ab^2
=> b^2 = 1 ( vì a,b khác 0 )
=> b=+-1
+, Nếu b=-1
Có : ab = a+b
=> -a = a+1
=> a=-1/2
=> T = 5/4
+, Nếu b = 1
Có : ab = a+b
=> a = a+1
=> ko tồn tại a t/m
Vậy T = 5/4
Tk mk nha
\(\dfrac{ab}{a+b}=\dfrac{bc}{b+c}=\dfrac{ca}{c+a}\)
\(\Rightarrow\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{c}+\dfrac{1}{a}\)
\(\Rightarrow\dfrac{1}{a}=\dfrac{1}{b}=\dfrac{1}{c}=\dfrac{1+1+1}{a+b+c}=\dfrac{3}{a+b+c}=\dfrac{3}{1}=3\)
\(\Rightarrow a=b=c=\dfrac{1}{3}\)
\(\Rightarrow A=\dfrac{a^3\left(a^2+b^2+c^2\right)}{a^2+b^2+c^2}=a^3=\left(\dfrac{1}{3}\right)^3=\dfrac{1}{27}\)
\(a,\dfrac{3}{a+b}=\dfrac{2}{b+c}=\dfrac{1}{c+a}\\ \Rightarrow\dfrac{a+b}{3}=\dfrac{b+c}{2}=\dfrac{c+a}{1}=\dfrac{2\left(a+b+c\right)}{6}=\dfrac{a+b+c}{3}\\ \Rightarrow\dfrac{a+b}{3}=\dfrac{a+b+c}{3}\\ \Rightarrow3\left(a+b+c\right)=3\left(a+b\right)\\ \Rightarrow3\left(a+b\right)+3c=3\left(a+b\right)\\ \Rightarrow3c=0\\ \Rightarrow c=0\)
Vậy \(P=\dfrac{a+b-2019c}{a+b+2018c}=\dfrac{a+b}{a+b}=1\)
Xét a+b+c=0 thì A=\(\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{\left(-c\right).\left(-a\right).\left(-b\right)}{abc}=-1\)
Xét a+b+c\(\ne0\).Áp dụng dãy tỉ số bằng nhau ta có:
\(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}=\frac{a+b+c}{b+c+a}=1\Rightarrow a=b=c\)
\(\Rightarrow A=\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}=\frac{2a.2a.2a}{a.a.a}=8\)
Vậy.................................