giải phuong trình
$(x+3\sqrt{x}+2)(x+9\sqrt{x}+18)=120x$
#2
Posted 10-10-2016 - 20:10
Isaac Newton
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Binh nhì
ĐK: $x\geq 0$
x=0 không thỏa mãn.
Xét x khác 0.
$(x+3\sqrt{x}+2)(x+9\sqrt{x}+18)=120x$
$\Leftrightarrow (\sqrt{x}+1)(\sqrt{x}+2)\sqrt{x}+3)(\sqrt{x}+6)=120x \Leftrightarrow (x+7\sqrt{x}+6)(x+5\sqrt{x}+6)=120x \Leftrightarrow (\sqrt{x}+\frac{6}{\sqrt{x}}+7)(\sqrt{x}+\frac{6}{\sqrt{x}}+5)=120\Leftrightarrow (t-1)(t+1)=120\Leftrightarrow t=11$
Với $t=\sqrt{x}+\frac{6}{\sqrt{x}}+6 (t>0)$...
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#3
Posted 12-10-2016 - 15:06
Lou Lou
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Lính mới
ĐKXĐ : x $\geq 0$
Ta có PT <=>$(\sqrt{x}+1)(\sqrt{x}+2)(\sqrt{x}+3)(\sqrt{x}+6)$
$\left [ (\sqrt{x}+1)(\sqrt{x}+6) \right ]\left [ (\sqrt{x}+2)(\sqrt{x}+3) \right ]$
$(x+7\sqrt{x}+6)(x+5\sqrt{x}+6)$
Đặt $x+5\sqrt{x}+6=m => pt<=> m(m+2\sqrt{x})=120x$
sau đó tự giải nhé :3 
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