Violympic toán 7
Các câu hỏi tương tự
Cho \(\dfrac{a}{b}< \dfrac{c}{d}\)và b, d > 0 . CMR : \(\dfrac{a}{b}< \dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)
Biết \(\dfrac{a}{b}< \dfrac{c}{d}\left(b,d>0\right)\)
CMR \(\dfrac{a}{b}=\dfrac{ab+cd}{b^2+d^2}< \dfrac{c}{d}\)
biết:\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{ab}{cd}\) với a,b,c,d\(\ne\)0. CMR:
\(\dfrac{a}{b}=\dfrac{c}{d}\) hoặc \(\dfrac{a}{b}=\dfrac{d}{c}\)
\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}.CMR\left(\dfrac{a+b+c}{b+c+d}\right)^3=\dfrac{a}{d}\)
Bài 1
CMR: \(\dfrac{a}{c}=\dfrac{c}{b}=\dfrac{b}{d}cmr:\dfrac{a^3+c^3-b^3}{c^3+b^3-d^3}=\dfrac{a}{d}\)
Cho a+b+c+d\(\ne\)0 và \(\dfrac{a}{b+c+d}=\dfrac{b}{a+c+d}=\dfrac{c}{a+b+d}=\dfrac{d}{a+b+c}\)
Tìm giá trị của A=\(\dfrac{a+b}{c+d}=\dfrac{b+c}{a+d}=\dfrac{c+d}{a+b}=\dfrac{d+a}{b+c}\)
Cho dfrac{a}{b}dfrac{c}{d}.CMR
a, dfrac{a+c}{b+d}dfrac{a-c}{b-d}
b, dfrac{c}{a+c}dfrac{b}{b+d}
c, dfrac{a+b}{a}dfrac{d}{c+d}
d, dfrac{2a+3c}{2b+3d}dfrac{2a-3c}{2b-3d}
e, dfrac{4a-3b}{a}dfrac{4c-3d}{c}
f, dfrac{a^2+b^2}{a^2-b^2}dfrac{c^2+d^2}{c^2-d^2}
Đọc tiếp
Cho \(\dfrac{a}{b}=\dfrac{c}{d}.CMR\)
a, \(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\)
b, \(\dfrac{c}{a+c}=\dfrac{b}{b+d}\)
c, \(\dfrac{a+b}{a}=\dfrac{d}{c+d}\)
d, \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)
e, \(\dfrac{4a-3b}{a}=\dfrac{4c-3d}{c}\)
f, \(\dfrac{a^2+b^2}{a^2-b^2}=\dfrac{c^2+d^2}{c^2-d^2}\)
Cho a,b,c,d \(\ne\) 0 thỏa mãn:
\(\dfrac{b+c+d}{a}=\dfrac{c+d+a}{b}=\dfrac{a+b+d}{c}=\dfrac{a+b+c}{d}\)
Tính \(M=\dfrac{a+b}{c+d}+\dfrac{b+c}{d+a}+\dfrac{c+d}{a+b}+\dfrac{d+a}{b+c}\)
cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{d}{a}\) với a+b+c+d ≠ 0. Tính giá trị biểu thức M = \(\dfrac{2a-b}{c+d}=\dfrac{2b-c}{d+a}=\dfrac{2c-d}{a+b}=\dfrac{2d-a}{b+c}\)
cho dfrac{b}{a}dfrac{c}{d}cmr:
a,dfrac{a}{a-b}dfrac{c}{c-d}
b,dfrac{a}{b}dfrac{a+c}{b+d}
c,dfrac{a}{3a+b}dfrac{c}{3c+d}
d,dfrac{ac}{bd}dfrac{a^2+b^2}{b^2+d^2}
e,dfrac{a.b}{c.d}dfrac{a^2-b^2}{c^2-d^2}
f,dfrac{a.b}{c.d}dfrac{left(a-bright)^2}{left(c-dright)^2}
Đọc tiếp
cho \(\dfrac{b}{a}=\dfrac{c}{d}\)cmr:
a,\(\dfrac{a}{a-b}=\dfrac{c}{c-d}\)
b,\(\dfrac{a}{b}=\dfrac{a+c}{b+d}\)
c,\(\dfrac{a}{3a+b}=\dfrac{c}{3c+d}\)
d,\(\dfrac{ac}{bd}=\dfrac{a^2+b^2}{b^2+d^2}\)
e,\(\dfrac{a.b}{c.d}=\dfrac{a^2-b^2}{c^2-d^2}\)
f,\(\dfrac{a.b}{c.d}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)