Câu hỏi của Evil

Question

1.Cho ab/b = bc/c=ca/a. Tính A= (a-b)(b-c)(c-a) + 20162. Cho (ab + bc)/ ( a+b) = ( bc + ca )/(b+c)= ( ca + ab) / (c+a)Tính M=\(\left(\frac{b}{a}+1\right)\left(\frac{c}{b}+1\right)\left(\frac{a}{c}+1\r...

Phùng Minh Quân · Accepted Answer

$1)$$\frac{\overline{ab}}{b}=\frac{\overline{bc}}{c}=\frac{\overline{ca}}{a}$$\Leftrightarrow$$\frac{10a+b}{b}=\frac{10b+c}{c}=\frac{10c+a}{a}$$\Leftrightarrow$$\frac{10a}{b}=\frac{10b}{c}=\frac{10c}{a}$Áp dụng tính chất dãy tỉ số bằng nhau ta có : $\frac{10a}{b}=\frac{10b}{c}=\frac{10c}{a}=\frac{10a+10b+10c}{a+b+c}=\frac{10\left(a+b+c\right)}{a+b+c}=10$Do đó : $\frac{10a}{b}=10$$\Leftrightarrow$$a=b$$\frac{10b}{c}=10$$\Leftrightarrow$$b=c$$\frac{10c}{a}=10$$\Leftrightarrow$$c=a$$\Rightarrow$$a=b=c$$\Rightarrow$$A=\left(a-b\right)\left(b-c\right)\left(c-a\right)+2016=2016$$2)$$\frac{\overline{ab}+\overline{bc}}{a+b}=\frac{\overline{bc}+\overline{ca}}{b+c}=\frac{\overline{ca}+\overline{ab}}{c+a}$Áp dụng tính chất dãy tỉ số bằng nhau ta có : $\frac{\overline{ab}+\overline{bc}}{a+b}=\frac{\overline{bc}+\overline{ca}}{b+c}=\frac{\overline{ca}+\overline{ab}}{c+a}=\frac{2\left(\overline{ab}+\overline{bc}+\overline{ca}\right)}{2\left(a+b+c\right)}=\frac{\overline{ab}+\overline{bc}+\overline{ca}}{a+b+c}$$=\frac{10a+b+10b+c+10c+a}{a+b+c}=\frac{11a+11b+11c}{a+b+c}=\frac{11\left(a+b+c\right)}{a+b+c}=11$Do đó : $\frac{\overline{ab}+\overline{bc}}{a+b}=11$$\Leftrightarrow$$10a+11b+c=11a+11b$$\Leftrightarrow$$c=a$$\frac{\overline{bc}+\overline{ca}}{b+c}=11$$\Leftrightarrow$$10b+11c+a=11b+11c$$\Leftrightarrow$$a=b$$\frac{\overline{ca}+\overline{ab}}{c+a}=11$$\Leftrightarrow$$10c+11a+b=11c+11a$$\Leftrightarrow$$b=c$$\Rightarrow$$a=b=c$$\Rightarrow$$M=\left(\frac{b}{a}+1\right)\left(\frac{c}{b}+1\right)\left(\frac{a}{c}+1\right)+2016=2.2.2+2016=2024$Chúc bạn học tốt ~ Câu trả lời: $1)$$\frac{\overline{ab}}{b}=\frac{\overline{bc}}{c}=\frac{\overline{ca}}{a}$$\Leftrightarrow$$\frac{10a+b}{b}=\frac{10b+c}{c}=\frac{10c+a}{a}$$\Leftrightarrow$$\frac{10a}{b}=\frac{10b}{c}=\frac{10c}{a}$Áp dụng tính chất dãy tỉ số bằng nhau ta có : $\frac{10a}{b}=\frac{10b}{c}=\frac{10c}{a}=\frac{10a+10b+10c}{a+b+c}=\frac{10\left(a+b+c\right)}{a+b+c}=10$Do đó : $\frac{10a}{b}=10$$\Leftrightarrow$$a=b$$\frac{10b}{c}=10$$\Leftrightarrow$$b=c$$\frac{10c}{a}=10$$\Leftrightarrow$$c=a$$\Rightarrow$$a=b=c$$\Rightarrow$$A=\left(a-b\right)\left(b-c\right)\left(c-a\right)+2016=2016$$2)$$\frac{\overline{ab}+\overline{bc}}{a+b}=\frac{\overline{bc}+\overline{ca}}{b+c}=\frac{\overline{ca}+\overline{ab}}{c+a}$Áp dụng tính chất dãy tỉ số bằng nhau ta có : $\frac{\overline{ab}+\overline{bc}}{a+b}=\frac{\overline{bc}+\overline{ca}}{b+c}=\frac{\overline{ca}+\overline{ab}}{c+a}=\frac{2\left(\overline{ab}+\overline{bc}+\overline{ca}\right)}{2\left(a+b+c\right)}=\frac{\overline{ab}+\overline{bc}+\overline{ca}}{a+b+c}$$=\frac{10a+b+10b+c+10c+a}{a+b+c}=\frac{11a+11b+11c}{a+b+c}=\frac{11\left(a+b+c\right)}{a+b+c}=11$Do đó : $\frac{\overline{ab}+\overline{bc}}{a+b}=11$$\Leftrightarrow$$10a+11b+c=11a+11b$$\Leftrightarrow$$c=a$$\frac{\overline{bc}+\overline{ca}}{b+c}=11$$\Leftrightarrow$$10b+11c+a=11b+11c$$\Leftrightarrow$$a=b$$\frac{\overline{ca}+\overline{ab}}{c+a}=11$$\Leftrightarrow$$10c+11a+b=11c+11a$$\Leftrightarrow$$b=c$$\Rightarrow$$a=b=c$$\Rightarrow$$M=\left(\frac{b}{a}+1\right)\left(\frac{c}{b}+1\right)\left(\frac{a}{c}+1\right)+2016=2.2.2+2016=2024$Chúc bạn học tốt ~

tth_new · Answer

Ta có: $\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}$$\Rightarrow\frac{a}{b+c+d}+1=\frac{b}{a+c+d}+1=\frac{c}{a+b+d}+1=\frac{d}{a+b+c}+1$hay $\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{a+c+d}=\frac{a+b+c+d}{a+b+d}=\frac{a+b+c+d}{a+b+c}$Do các tử số trên bằng nhau nên các mẫu số cũng bằng nhau hay $b+c+d=a+c+d=a+b+d=a+b+c$Suy ra a = b =c =d$\Rightarrow A=\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=1+1+1+1=4$Câu trả lời: Ta có: $\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}$$\Rightarrow\frac{a}{b+c+d}+1=\frac{b}{a+c+d}+1=\frac{c}{a+b+d}+1=\frac{d}{a+b+c}+1$hay $\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{a+c+d}=\frac{a+b+c+d}{a+b+d}=\frac{a+b+c+d}{a+b+c}$Do các tử số trên bằng nhau nên các mẫu số cũng bằng nhau hay $b+c+d=a+c+d=a+b+d=a+b+c$Suy ra a = b =c =d$\Rightarrow A=\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=1+1+1+1=4$

Phùng Minh Quân · Answer

$3)$$\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}$$\Leftrightarrow$$\frac{a}{b+c+d}+1=\frac{b}{a+c+d}+1=\frac{c}{a+b+d}+1=\frac{d}{a+b+c}+1$$\Leftrightarrow$$\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{a+c+d}=\frac{a+b+c+d}{a+b+d}=\frac{a+b+c+d}{a+b+c}$Vì các tử bằng nhau nên mẫu cũng bằng nhau : +) Với $b+c+d=a+c+d$$\Leftrightarrow$$a=b$+) Với $a+b+d=a+b+c$$\Leftrightarrow$$c=d$+) Với $a+c+d=a+b+d$$\Leftrightarrow$$b=c$$\Rightarrow$$a=b=c=d$$\Rightarrow$$A=\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=1+1+1+1=4$Chúc bạn học tốt ~ Câu trả lời: $3)$$\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}$$\Leftrightarrow$$\frac{a}{b+c+d}+1=\frac{b}{a+c+d}+1=\frac{c}{a+b+d}+1=\frac{d}{a+b+c}+1$$\Leftrightarrow$$\frac{a+b+c+d}{b+c+d}=\frac{a+b+c+d}{a+c+d}=\frac{a+b+c+d}{a+b+d}=\frac{a+b+c+d}{a+b+c}$Vì các tử bằng nhau nên mẫu cũng bằng nhau : +) Với $b+c+d=a+c+d$$\Leftrightarrow$$a=b$+) Với $a+b+d=a+b+c$$\Leftrightarrow$$c=d$+) Với $a+c+d=a+b+d$$\Leftrightarrow$$b=c$$\Rightarrow$$a=b=c=d$$\Rightarrow$$A=\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}=1+1+1+1=4$Chúc bạn học tốt ~

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