Câu hỏi của Ngô Huy Hoàng

Question

cho$\frac{a}{b}=\frac{c}{d}$ chứng minh rằng

$\frac{7a^2+3ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}$

Hoàng Xuân Ngân · Accepted Answer

$\frac{a}{b}=\frac{c}{d}$

$=>\frac{a}{c}=\frac{b}{d}$

$=>\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}$

$=>\frac{7a^2}{7c^2}=\frac{11a^2}{11c^2}=\frac{8b^2}{8d^2}=\frac{3ab}{3cd}$

$=>\frac{7a^2+3ab}{7c^2+cd}=\frac{11a^2-8b^2}{11c^2-8d^2}$

$=>\frac{7a^2+3ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}$(ĐPCM)

Câu trả lời:

$\frac{a}{b}=\frac{c}{d}$

$=>\frac{a}{c}=\frac{b}{d}$

$=>\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}$

$=>\frac{7a^2}{7c^2}=\frac{11a^2}{11c^2}=\frac{8b^2}{8d^2}=\frac{3ab}{3cd}$

$=>\frac{7a^2+3ab}{7c^2+cd}=\frac{11a^2-8b^2}{11c^2-8d^2}$

$=>\frac{7a^2+3ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}$(ĐPCM)