Giải pt sau:
[tex]5\sqrt{x-1}+9\sqrt{x+1}= 8x+6[/tex]
@Nữ Thần Mặt Trăng @Thiên Thuận @bonechimte@gmail.com
ĐK: $x\ge 1$
pt $\Leftrightarrow 5\sqrt{x-1}-\dfrac 52+9\sqrt{x+1}-\dfrac{27}2-8x+10=0$
$\Leftrightarrow \dfrac{5(x-\dfrac 54)}{\sqrt{x-1}+2,5}+\dfrac{9(x-\dfrac 54)}{\sqrt{x+1}+13,5}-8(x-\dfrac 54)=0$
$\Leftrightarrow (x-\dfrac 54)(\dfrac{5}{\sqrt{x-1}+2,5}+\dfrac{9}{\sqrt{x+1}+13,5}-8)=0$
Mà $\dfrac{5}{\sqrt{x-1}+2,5}+\dfrac{9}{\sqrt{x+1}+13,5}-8\le \dfrac{5}{2,5}+\dfrac{9}{\sqrt 2+13,5}-8<0$
$\Rightarrow x-\dfrac 54=0\Leftrightarrow x=\dfrac 54$ (TM)
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