Question

\(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

Answer 1

\(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

⇔ \(\sqrt{2x-5+2.3\sqrt{2x-5}+9}+\sqrt{2x-5-2\sqrt{2x-5}+1}=4\)

⇔ \(\text{ |}\sqrt{2x-5}+3\text{ |}+\text{ |}\sqrt{2x-5}-1\text{ |}=4\)

⇔ \(\sqrt{2x-5}+3+\text{ |}\sqrt{2x-5}-1\text{ |}=4\) ( x ≥ \(\dfrac{5}{2}\) ) ( 1)

+) Với : \(\sqrt{2x-5}\text{≥}1\) ⇔ x ≥ 3 , ta có :

\(\left(1\right)\text{⇔}\sqrt{2x-5}+3+\sqrt{2x-5}-1=4\)

\(\text{⇔}2\sqrt{2x-5}=2\)

\(\text{⇔}x=3\left(TM\right)\)

+) Với : \(\sqrt{2x-5}< 1\) ⇔ x < 3 , ta có :

\(\left(1\right)\text{⇔}\sqrt{2x-5}+3+1-\sqrt{2x-5}=4\)

\(\text{⇔}4=4\) ( luôn đúng với : \(3>x\text{≥}\dfrac{5}{2}\) )

KL...............