Lam lai nha , nay cau tha qua :(
\(\sqrt{x-5}-\dfrac{x-14}{3+\sqrt{x-5}}=3\) ( x ≥ 5 )
Dat : \(\sqrt{x-5}=a\) ( x ≥ 0 ) , ta co :
\(\sqrt{a}-\dfrac{a-9}{3+\sqrt{a}}=3\)
⇔ \(\sqrt{a}-\sqrt{a}+3=3\)
⇔ \(3=3\left(Luon-dung\right)\)
KL........
\(\sqrt{x-5}-\dfrac{x-14}{3+\sqrt{x-5}}=3\)
\(\sqrt{x-5}-\dfrac{x-14}{3+\sqrt{x-5}}=3,x\in\left[5,+\infty\right]\)
\(\sqrt{x-5}-\dfrac{x-14}{3+\sqrt{x-5}}-3=0\)
\(\dfrac{\left(3+\sqrt{x-5}\right)\sqrt{x-5}-\left(x-14\right)-3\left(3+\sqrt{x-5}\right)}{3+\sqrt{x-5}}=0\)
\(3\sqrt{x-5}\sqrt{x-5}-\left(x-14\right)-3\left(3+\sqrt{x-5}\right)=0\)
\(3\sqrt{x-5}+x-5-\left(x-14\right)-9-3\sqrt{x-5}=0\)
\(x-5-x+14-9=0\)
\(0=0\)
\(x\in R,x\in\left[5,+\infty\right]\)
Cach khac :3
\(\sqrt{x-5}-\dfrac{x-14}{3+\sqrt{x-5}}=3\) ( x ≥ 5)
Dat : \(x-5=a\) ( a ≥ 0 ), ta co :
\(\sqrt{a}+\dfrac{a-9}{3+\sqrt{a}}=3\)
⇔ \(\sqrt{a}+\dfrac{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}{\sqrt{a}+3}=3\)
\(\text{⇔}2\sqrt{a}=6\)
⇔ \(\sqrt{a}=3\text{⇔}a=9\) ( TM )
Khi do : \(x-5=9\text{⇔}x=14\left(TM\right)\)
KL..............
