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

Ta có \(\frac{a}{c}=\frac{c}{b}\)

=> c² = ab

a) Ta có: \(\frac{a^{2} + c^{2}}{b^{2} + c^{2}}= \frac{a^{2} + ab}{b^{2} + ab}\) = \(\frac{a\left ( a + b \right )}{b(a + b)}= \frac{a}{b}\) (đpcm)

b) Ta có: \(\frac{b^{2} - a^{2}}{a^{2} + c^{2}}= \frac{\left ( b - a \right )\left ( b + a \right )}{a^{2} + ab}= \frac{\left ( b - a \right )\left ( b + a \right )}{a\left ( b + a \right )}= \frac{b - a}{a}\) (đpcm)

b² - a² = (b - a)(b + a) đây là HĐT nhé có dạng: A² - B² = (A - B)(A + B)