Giải các phương trình sau:
a) $\sqrt{3x-2}$ + $\sqrt{x-1}$  = 4x -9 + 2$\sqrt{3x^{2}-5x+2}$
b) $3\sqrt{2+x}$ - $6\sqrt{2-x}$ + 4$\sqrt{4-x^{2}}$ = 10 - 3x
Tìm m để pt : $\sqrt{1+x}$ +  $\sqrt{8-x}$ = $\sqrt{-x^{2}+7x+8}$ + m có nghiệm

m nghĩ x-1 thì nó ms đúng –  ๖ۣۜTQT☾♋☽ 20-12-16 11:11 PM
a,đặt vế trái bằng $t(t\geq0)\Rightarrow t^2=4x-3+2\sqrt{3x^2-5x+2}$
$\Rightarrow pt\Leftrightarrow t=t^2-6\Leftrightarrow (t-3)(t+2)=0$(sau đó thay t tìm x đc kq x=2)
b,đặt$: t=\sqrt{x+2}+2\sqrt{2-x}(t\geq 0)\Rightarrow t^2=10-3x-2\sqrt{4-x^2}(ôi-đẹp-quá-con-ơi)$
$\Rightarrow$ pt trở thành$:2t=t^2\Leftrightarrow t(t-2)=0$(thế vào rồi tính)
sai rồi b ơi. –  nhokkaitoo 22-12-16 05:13 AM
m có thấy sao đâu –  ๖ۣۜTQT☾♋☽ 22-12-16 04:02 AM
Thái quá =.= –  Confusion 21-12-16 07:28 AM
bạn coi lại dùm mk đc ko ạ?? có vẻ hơi sai sai sao í. Thanks :)) –  nhokkaitoo 21-12-16 06:25 AM
Đặt $t=\sqrt{1+x} +\sqrt{8-x}  ; t \in  \left[3 {;}3\sqrt{2} \right]\Rightarrow t^{2}=9+2\sqrt{-x^{2}+7x+8}$
$\Rightarrow \sqrt{-x^{2}+7x+8}=\frac{t^{2}-9}{2}$
pt $\Leftrightarrow t=\frac{t^{2}-9}{2}+m$
$\Leftrightarrow 2t-t^{2}+9=2m$
lập BBT $\Rightarrow m\in \left[ \frac{-9+6\sqrt{2}}{2}{;}3 \right]$
camon :) –  nhokkaitoo 22-12-16 05:14 AM

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