cho a;b;c;d \(\in\) \(ℕ^∗\)thoa man \(\frac{a}{b}< \frac{c}{d}\)chúng minh rang \(\frac{2018a+c}{2018b+d}< \frac{c}{d}\)
1) Cho 2 phan so \(\frac{a}{b}=\frac{c}{d}\)
Chung to: \(\left[\frac{a-b}{c-d}\right]^4\) = \(\frac{a^4+b^4}{c^4+d^4}\)
Cac ban giai chi tiet vao nha! Thank you
Cho B=\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)Hay chung to rang B>1
cho \(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)
chung to rang B >1
Cho a + b + c + d khác 0 và \(\frac{a}{b+c+d}=\frac{b}{a+c+d}=\frac{c}{a+b+d}=\frac{d}{a+b+c}\)
Tính giá trị biểu thức \(A=\frac{a+b}{c+d}+\frac{b+c}{a+d}+\frac{c+d}{a+b}+\frac{d+a}{b+c}\)
cho a,b,c,d thoả mãn \(\frac{a}{b+c+d}+\frac{b}{c+d+a}+\frac{c}{d+a+b}+\frac{d}{a+b+c}=1\)
Tính \(\frac{a^2}{b+c+d}+\frac{b^2}{c+d+a}+\frac{c^2}{d+a+b}+\frac{d^2}{a+b+c}\)
\(a,b,c,d\in N\)nhỏ nhất sao cho \(\frac{a}{b}=\frac{3}{5};\frac{b}{c}=\frac{4}{7};\frac{c}{d}=\frac{6}{11}\)
a) \(\frac{a}{a+b+c}+\frac{b}{b+c+d}+\frac{c}{c+d+a}+\frac{d}{d+a+b}\)= ?
b) Tìm các STN a, b, c, d (khác nhau) sao cho :
\(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{d^2}=1\)
Cho \(\frac{a}{b}=\frac{c}{d}\)( b,d khác 0). CMR
a) \(\frac{a-b}{a}=\frac{c-d}{c}\)
b) \(\frac{a}{a+b}=\frac{c}{c+d}\)
c) \(\frac{a}{a-b}=\frac{c}{c-d}\)