Question

Cho a/b=c/d,Chứng minh: \(\frac{7a^2+ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}\)

Answer 1

\(dat\frac{a}{b}=\frac{c}{d}=k\)->> a=b.k va c=d.k

về phai

\(\frac{7.\left(d.k\right)^2+d.k.d}{11.\left(d.k\right)^2-8.d^2}=\frac{d^2.k\left(7k+1\right)}{d^2.\left(11k^2-8\right)}=\frac{k.\left(7k+1\right)}{11k^2-8}\)

ve trai

\(\frac{7.\left(b.k\right)^2+b.k.b}{11.\left(b.k\right)^2-8b^2}=\frac{b^2k.\left(7k+1\right)}{b^2.\left(11k^2-8\right)}=\frac{k.\left(7k+1\right)}{11k^2-8}\)

vậy vế trái = vế phải --> dpcm ( để bạn ghi có sai cho 3.cd k??_)