5/2= y/x và x+y =-21
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ta có:
\(\frac{x}{5}=\frac{y}{2}\)và\(x+y=-21\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{5}=\frac{y}{2}=\frac{x+y}{5+2}=-\frac{21}{7}=-3\)
\(=>\frac{x}{5}=-3=>x=-15\)
\(\frac{y}{2}=-3=>y=-6\)
Vậy x=-15 và y=-6
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⇒ab+c+d+1=bc+d+a+1=cd+a+b+1=da+b+c+1⇒ab+c+d+1=bc+d+a+1=cd+a+b+1=da+b+c+1
⇒a+b+c+db+c+d=b+c+d+ac+d+a=c+d+a+bd+a+b=d+a+b+ca+b+c⇒a+b+c+db+c+d=b+c+d+ac+d+a=c+d+a+bd+a+b=d+a+b+ca+b+c
Xét a+b+c+d≠0a+b+c+d≠0 suy ra a=b=c=da=b=c=d. Khi đó:
P=a+bc+d+b+cd+a+c+db+a+d+ab+c=1+1+1+1=4P=a+bc+d+b+cd+a+c+db+a+d+ab+c=1+1+1+1=4
Xét a+b+c+d=0a+b+c+d=0 suy ra ⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩a+b=−(c+d)b+c=−(d+a)c+d=−(b+a)d+a=−(b+c){a+b=−(c+d)b+c=−(d+a)c+d=−(b+a)d+a=−(b+c). Khi đó:
P=a+bc+d+b+cd+a+c+db+a+d+ab+c=(−1)+(−1)+(−1)+(−1)=−4
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\(\frac{5}{2}=\frac{x}{y}=\frac{y}{2}=\frac{x}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có :
\(\frac{x}{5}=\frac{y}{2}=\frac{x+y}{5+2}=-\frac{21}{7}=-3\)
+)\(\frac{x}{5}=-3\Rightarrow x=-3.5=-15\)
+)\(\frac{y}{2}=-3\Rightarrow y=-3.2=-6\)