Cùng chia 2 vế BĐT cho $\sqrt{ab}$ , ta có : P= $\sqrt{\frac{c}{b}\times \frac{a-c}{a}}+\sqrt{\frac{c}{a}\times\frac{b-c}{b} } \leq 1$$P\leq \frac{\frac{c}{b}+\frac{a-c}{a}}{2}+\frac{\frac{c}{a}+\frac{b-c}{b}}{2}= \frac{\frac{c}{b}+1-\frac{c}{a}+1- \frac{c}{b}}{2}=1$ => đpcmĐẳng thức xảy ra khi $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$
Cùng chia 2 vế BĐT cho $\sqrt{ab}$ , ta có : P= $\sqrt{\frac{c}{b}\times \frac{a-c}{a}}+\sqrt{\frac{c}{a}\times\frac{b-c}{b} } \leq 1$$P\leq \frac{\frac{c}{b}+\frac{a-c}{a}}{2}+\frac{\frac{c}{a}+\frac{b-c}{b}}{2}= \frac{\frac{c}{b}+1-\frac{c}{a}+1- \frac{c}{b}}{2}=1$ => ĐPCMĐẳng thức xảy ra khi $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$
Cùng chia 2 vế BĐT cho $\sqrt{ab}$ , ta có : P= $\sqrt{\frac{c}{b}\times \frac{a-c}{a}}+\sqrt{\frac{c}{a}\times\frac{b-c}{b} } \leq 1$$P\leq \frac{\frac{c}{b}+\frac{a-c}{a}}{2}+\frac{\frac{c}{a}+\frac{b-c}{b}}{2}= \frac{\frac{c}{b}+1-\frac{c}{a}+1- \frac{c}{b}}{2}=1$ =>
đpcmĐẳng thức xảy ra khi $\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$