Giải thích các bước giải:
a.Ta có:
$\dfrac{AB^2}{AC^2}=\dfrac{BH\cdot BC}{CH\cdot CB}=\dfrac{BH}{CH}$
$\to (\dfrac{AB^2}{AC^2})^2=(\dfrac{BH}{CH})^2$
$\to \dfrac{AB^4}{AC^4}=\dfrac{BH^2}{CH^2}=\dfrac{BI\cdot BA}{CK\cdot CA}$
$\to \dfrac{AB^3}{AC^3}=\dfrac{BI}{CK}$
b.Ta có:
$\Delta ABC$ vuông tại $A, AH\perp BC\to AH^2=HB\cdot HC$
$\to AH^4=(HB\cdot HC)^2$
$\to AH^4=HB^2\cdot HC^2$
$\to AH^4=(BI\cdot BA)\cdot (CK\cdot CA)$
$\to AH^4=(BI\cdot CK)\cdot (BA\cdot CA)$
$\to AH^4=(BI\cdot CK)\cdot (AH\cdot BC)$
$\to AH^3=BI\cdot CK\cdot BC$
$\to \sqrt{BH\cdot HC}=AH=\sqrt[3]{BI\cdot CK\cdot BC}$
