cho a,b khac 0 thoa man dang thuc: (a^3+b^3)^2=(a^2+b^2)^3. hoi a/b+b/a=
Cho 3 so a,b,c khac 0 thoa man ab/a+b=bc/b+c=ca/c+a
Tinh gia tri cua bieu thuc M=ab+bc+ca/a^2+b^2+c^2
cho cac so thuc a, b,c khac 0 thoa man a^2*(a+b)=b^2*(b+c)=2016. tinh bieu thuc A=c^2*(a+c)
cho 3 so thuc abc khac 0 va mot doi so khac nhau thoa man
a2 . ( b+ c ) = b2 . ( a + c ) = 2018
Tinh gia tri bieu thuc H = c2 . ( a+b)
Cho 3 so a,b,c khac 0 va doi mot khac nhau thoa man a^2.(b+c)=b^2.(a+c)=2015 Tinh c^2.(a+b)
Cho a.b,c la 3 so khac 0 thoa man : ab + a + b / a + b = bc + b + c / b + c = ca + c + a/ c + a ( voi gia thiet cac ti so deu co nghia)
Tinh gia tri bieu thuc M = ab+bc+ca+2017/ a^2 + b^2 + c^2 + 2017
cho 2 so thuc a va b khac 0 thoa man 2a2 +b2/4 +1/a2=4
cho 3 so a,b,c khac 0 va thoa man a+b-c/c=a+c-b/b=b+c-a/a
tinh gia tri bieu thuc P=(a+b)(b+c)(c+a)=abc
Ta có : \(\frac{a+b-c}{c}=\frac{a+c-b}{b}=\frac{b+c-a}{a}\)
\(\Rightarrow\frac{a+b}{c}-\frac{c}{c}=\frac{a+c}{b}-\frac{b}{b}=\frac{b+c}{a}-\frac{a}{a}\)
\(\frac{a+b}{c}-1=\frac{c+b}{a}-1=\frac{a+c}{b}-1\)
\(\Rightarrow\frac{a+b}{c}=\frac{b+c}{a}=\frac{a+c}{b}\)
Áp dụng tính chất của dãy tỉ số bằng nhau , ta có
\(\frac{a+b}{c}=\frac{b+c}{a}=\frac{a+c}{b}=\frac{2a+2b+2c}{a+b+c}=\frac{2\left(a+b+c\right)}{a+b+c}=2\)
\(\Rightarrow\hept{\begin{cases}a+b=2c\\b+c=2a\\a+c=2b\end{cases}}\)
Vậy \(P=\left(a+b\right)\left(b+c\right)\left(c+a\right)=2c.2a.2b=8abc\)
mà \(\left(a+b\right)\left(b+c\right)\left(c+a\right)=abc\Rightarrow8abc=abc\Rightarrow abc=0\Rightarrow P=0\)
cho a,b,c la ba so thuc khac nhau doi mot thoa man a^2(b+c)=b^2(a+c)=2015.Tinh c^2(a+b)
Cho 4 so a,b,c,d khac 0 thoa man;b^2=ac,c^2=bd,b^3+c^3+d^3 khac 0
CMR;a^3+b^3+c^3/b^3+c^3+d^3=a/d