Question

Chứng minh rằng \(\frac{a}{b}=\frac{c}{d}\) thì \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)

Answer 1

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

=>a=b.k

c=d.k

ta có Vế Phải : \(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(b.k\right)^2+b^2}{\left(d.k\right)^2+d^2}=\frac{b^2.k^2+b^2}{d^2.k^2+d^2}=\frac{b^2.\left(k^2+1\right)}{d^2.\left(k^2+1\right)}=\frac{b^2}{d^2}\)

Vế Trái :\(\frac{ab}{cd}=\frac{b.k.b}{d.k.d}=\frac{b^2.k}{d^2.k}=\frac{b^2}{d^2}\)

vì \(\frac{b^2}{d^2}=\frac{b^2}{d^2}\)

=>VP=VT

=>\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)

Answer 2

Đặt \(\frac{a}{b}=\frac{c}{d}=k\)

=> a=b.k; c=d.k

Suy ra:

\(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(b.k\right)^2+b^2}{\left(d.k\right)^2+d^2}=\frac{b^2}{d^2}\) (1)

\(\frac{ab}{cd}=\frac{b.k.b}{d.k.d}=\frac{b^2}{d^2}\) (2)

Từ (1) và (2) => \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)

Chúc bạn học tốt!

Answer 3

"." là nhân nha