a) 2x=3y=4z⇒\(\dfrac{2}{\dfrac{1}{x}}=\dfrac{3}{\dfrac{1}{y}}=\dfrac{4}{\dfrac{1}{z}}=\dfrac{2+3+4}{\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}}=\dfrac{9}{3}=3\) ( Vì\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=3\))
⇒ x=\(\dfrac{3}{2}\) ; y=1; z=\(\dfrac{3}{4}\)
b) \(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-by}{c}\)
= \(\dfrac{abz-acy}{a^{2^{ }}}=\dfrac{bcx-abz}{b^{2^{ }}}=\dfrac{acy-bcy}{c^2}\) =\(\dfrac{\left(abz-acy\right)+\left(bcx-abz\right)+\left(acy-bcy\right)}{a^2+b^2+c^{2^{ }}}=\dfrac{0}{a^2+b^2+c^{2^{ }}}=0\)
⇒\(\dfrac{bz-cy}{a}=\dfrac{cx-az}{b}=\dfrac{ay-by}{c}=0\)
⇒ ✽bz-cy=0⇒bz=cy⇒\(\dfrac{b}{y}=\dfrac{c}{z}\) (1)
✽ cx-az=0⇒cx=az⇒ \(\dfrac{a}{x}=\dfrac{c}{z}\) (2)
Từ (1) và (2) suy ra\(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)