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Hung nguyen, Trần Thanh Phương, Sky SơnTùng, @tth_new, @Nguyễn Việt Lâm, @Akai Haruma, @No choice teen
help me, pleaseee
Cần gấp lắm ạ!
c1 cậu đặt cái trong căn =a
=>pt<=> a^2-2x=2xa-a
c2 cậu đưa về dang a^2=b^2
bài 2 nhé
đặt \(a=\sqrt{x+2}\)
ta có pt<=>
\(2a^3=3x\left(x+2\right)-x^3\Leftrightarrow2a^3=3xa^2-x^3\)
\(\Leftrightarrow2a^3-3xa^2+x^3=0\Leftrightarrow2a^3-2a^2x+x^2-xa^2=0\)
\(\Leftrightarrow\left(a-x\right)\left(2a^2-ax-x^2\right)\)
a/ \(\Rightarrow2x^2-3x-11=x^2-1\)
\(\Leftrightarrow x^2-3x-10=0\Rightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)
Thay 2 nghiệm vào cả 2 căn thức thấy đều xác định
Vậy nghiệm của pt là ...
b/ \(\left\{{}\begin{matrix}x\ge-1\\2x^2+3x-5=\left(x+1\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x^2+x-6=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\ge-1\\\left[{}\begin{matrix}x=2\\x=-3\left(l\right)\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow x=2\)
c/
\(\Leftrightarrow x^2+4x+4=3x^2-5x+14\)
\(\Leftrightarrow2x^2-9x+10=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\frac{5}{2}\end{matrix}\right.\)
d/
\(\Leftrightarrow\left\{{}\begin{matrix}-x-9\ge0\\\left(x-1\right)\left(2x-3\right)=\left(-x-9\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le-9\\2x^2-5x+3=x^2+18x+81\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le-9\\x^2-23x-78=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=26\left(ktm\right)\\x=-3\left(ktm\right)\end{matrix}\right.\)
Vậy pt vô nghiệm
Câu 1 là \(\left(8x-4\right)\sqrt{x}-1\) hay là \(\left(8x-4\right)\sqrt{x-1}\)?
Câu 1:ĐK \(x\ge\frac{1}{2}\)
\(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
<=> \(\left(4x^2-3x-1\right)+4\left(2x-1\right)\sqrt{x}-2\sqrt{\left(2x-1\right)\left(x+3\right)}\)
<=> \(\left(x-1\right)\left(4x+1\right)+2\sqrt{2x-1}\left(2\sqrt{x\left(2x-1\right)}-\sqrt{x+3}\right)=0\)
<=> \(\left(x-1\right)\left(4x+1\right)+2\sqrt{2x-1}.\frac{8x^2-4x-x-3}{2\sqrt{x\left(2x-1\right)}+\sqrt{x+3}}=0\)
<=>\(\left(x-1\right)\left(4x+1\right)+2\sqrt{2x-1}.\frac{\left(x-1\right)\left(8x+3\right)}{2\sqrt{x\left(2x-1\right)}+\sqrt{x+3}}=0\)
<=> \(\left(x-1\right)\left(4x+1+2\sqrt{2x-1}.\frac{8x+3}{2\sqrt{x\left(2x-1\right)}+\sqrt{x+3}}\right)=0\)
Với \(x\ge\frac{1}{2}\)thì \(4x+1+2\sqrt{2x-1}.\frac{8x-3}{2\sqrt{x\left(2x-1\right)}+\sqrt{x+3}}>0\)
=> \(x=1\)(TM ĐKXĐ)
Vậy x=1
2,\(pt\Leftrightarrow12\left(\sqrt{x+1}-2\right)+x^2+x-12=0\)
\(\Leftrightarrow12\cdot\frac{x-3}{\sqrt{x+1}+2}+\left(x-3\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{12}{\sqrt{x+1}+2}+x+4\right)=0\)
Vì \(\left(\frac{12}{\sqrt{x+1}+2}+x+4\right)\ge0\left(\forall x>-1\right)\)
\(\Rightarrow x=3\)
ĐKXĐ: x∈R
\(\left(x+1\right)\left(2\sqrt{x^2+3}-x^2\right)+\sqrt[3]{3x^2+5}=5x+3\)
=>\(\left(x+1\right)\left(2\sqrt{x^2+3}-x^2\right)+\sqrt[3]{3x^2+5}-5x-3=0\)
=>\((x + 1)\left(2\sqrt{x^2 + 3} - x^2 - 3\right) + \left(\sqrt[3]{3x^2 + 5} - 2\right) - 2x + 2 = 0\)
\(\sqrt[3]{3x^2 + 5}-2\)
\(=\frac{3x^2 + 5 - 2^3}{\sqrt[3]{(3x^2+5)^2} + 2\sqrt[3]{3x^2+5} + 4}=\frac{3(x^2 - 1)}{\text{A}(x)}=\frac{3(x - 1)(x + 1)}{\text{A}(x)}\) , với A(x)=\(\sqrt[3]{(3x^2+5)^2}+2\sqrt[3]{3x^2+5}+4\)
\(2\sqrt{x^2 + 3}-(x^2+3)\)
\(=\frac{\left\lbrack2\sqrt{x^2 + 3}-(x^2+3)\right\rbrack\left\lbrack2\sqrt{x^2 + 3}+(x^2+3)\right\rbrack}{2\sqrt{x^2 + 3}+(x^2+3)}\)
=\(\frac{4(x^2 + 3) - (x^2 + 3)^2}{2\sqrt{x^2 + 3} + x^2 + 3}\quad\)
\(=\frac{\left(x^2+3\right)\left(4-x^2-3\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}=\frac{\left(x^2+3\right)\left(1-x\right)\left(1+x\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}\)
\((x+1)\left(2\sqrt{x^2 + 3}-x^2-3\right)+\left(\sqrt[3]{3x^2 + 5}-2\right)-2x+2=0\)
=>\(\left(x+1\right)\cdot\frac{\left(x^2+3\right)\left(1-x\right)\left(1+x\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}+\frac{3(x - 1)(x + 1)}{\text{A}(x)}-2\left(x-1\right)\) =0
=>(x-1)*G(x)=0
=>x-1=0
=>x=1(nhận)