Question

Cho : \(\dfrac{a}{c}=\dfrac{c}{b}.CMR:\\ a,\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{a}{b}\\ b,\dfrac{b^2-a^2}{a^2+c^2}=\dfrac{b-a}{a}\)

Answer 1

a, Từ \(\dfrac{a}{c}=\dfrac{c}{b}\Rightarrow c^2=a\cdot b\). Khi đó :

\(\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{a^2+a\cdot b}{b^2+a\cdot b}=\dfrac{a\cdot\left(a+b\right)}{b\cdot\left(a+b\right)}=\dfrac{a}{b}=VP\)

⇒ĐPCM

b, Từ \(\dfrac{a}{c}=\dfrac{c}{b}\Rightarrow c^2=a\cdot b\) và áp dụng công thức \(a^2-b^2=\left(a+b\right)\cdot\left(a-b\right)\).Khi đó :

\(\dfrac{b^2-a^2}{a^2+c^2}=\dfrac{\left(b-a\right)\left(b+a\right)}{a^2+a\cdot b}=\dfrac{\left(b-a\right)\left(a+b\right)}{a\cdot\left(a+b\right)}=\dfrac{b-a}{a}=VP\)

⇒ĐPCM