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Đặt \(\sqrt{2x^3+7}=a\)
=>6ax=3a^2+1+2x-4a
=>a=2x+1 hoặc a=1/3
=>2x^3+7=(2x+1)^2 hoặc 2x^3+7=1/3
=>\(x\in\left\{1;\dfrac{1-\sqrt{13}}{2};\sqrt[3]{-\dfrac{31}{9}}\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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Lời giải:
ĐKXĐ: $x\geq -3,5$
PT \(\Leftrightarrow (\sqrt{2x+7}-1)+(\sqrt[3]{x+4}-1)+(x^2+8x+15)=0\)
\(\Leftrightarrow \frac{2(x+3)}{\sqrt{2x+7}+1}+\frac{x+3}{\sqrt[3]{(x+4)^2}+\sqrt[3]{x+4}+1}+(x+3)(x+5)=0\)
\(\Leftrightarrow (x+3)\left[\frac{2}{\sqrt{2x+7}+1}+\frac{1}{\sqrt[3]{(x+4)^2}+\sqrt[3]{x+4}+1}+(x+5)\right]=0\)
Với $x\geq -3,5$ dễ thấy biểu thức trong ngoặc vuông $>0$
Do đó: $x+3=0$
$\Leftrightarrow x=-3$ (thỏa mãn)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\sqrt[3]{2x+4}=\dfrac{2x-1+5}{\sqrt[3]{\left(2x-1\right)^2}-\sqrt[3]{5\left(2x-1\right)}+\sqrt[3]{25}}\)
\(\Leftrightarrow\sqrt[3]{2x+4}=\dfrac{2x+4}{\sqrt[3]{\left(2x-1\right)^2}-\sqrt[3]{10x-5}+\sqrt[3]{25}}\)
=>\(\sqrt[3]{2x+4}\left(\dfrac{\sqrt[3]{\left(2x+4\right)^2}}{\sqrt[3]{\left(2x-1\right)^2}-\sqrt[3]{10x-5}+\sqrt[3]{25}}-1\right)=0\)
=>2x+4=0
=>x=-2
sory mik moi lop 8
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