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đề bài quá ẩu

\(x^4-25x^2+60x-36=0\)

\(\Leftrightarrow x^4+5x^3-6x^2-5x^3-25x^2+30x+6x^2+30x-36=0\)

\(\Leftrightarrow x^2\left(x^2+5x-6\right)-5x\left(x^2+5x-6\right)+6\left(x^2+5x-6\right)=0\)

\(\Leftrightarrow\left(x^2-5x+6\right)\left(x^2+5x-6\right)=0\)

\(\Leftrightarrow\left(x^2-2x-3x+6\right)\left(x^2-x+6x-6\right)=0\)

\(\Leftrightarrow\left[x\left(x-2\right)-3\left(x-2\right)\right]\left[x\left(x-1\right)+6\left(x-1\right)\right]=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+6\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\x-1=0\\x+6=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\\x=1\\x=-6\end{matrix}\right.\)

Cac ban giup mk di mk dang can ngay bay gio .

a.

\(\sqrt{4x^2+4x+1}-\sqrt{25x^2+10x+1}=0\)

\(\Leftrightarrow\sqrt{\left(2x+1\right)^2}-\sqrt{\left(5x+1\right)^2}=0\)

\(\Leftrightarrow2x+1-\left(5x+1\right)=0\)

\(\Leftrightarrow-3x=0\Leftrightarrow x=0\)

b.

\(\sqrt{x^4-16x^2+64}=\sqrt{25x^2+10x+1}\)

\(\Leftrightarrow\sqrt{\left(x^2-8\right)^2}=\sqrt{\left(5x+1\right)^2}\)

\(\Leftrightarrow x^2-8=5x+1\)

\(\Leftrightarrow x^2-5x+\dfrac{25}{4}=\dfrac{61}{4}\)

\(\Leftrightarrow\left(x-\dfrac{5}{2}\right)^2=\dfrac{61}{4}\)

............................

tương tự ..

c: \(\Leftrightarrow\sqrt{x-5}\left(\sqrt{x+5}-1\right)=0\)

=>x-5=0 hoặc x+5=1

=>x=-4 hoặc x=5

d: \(\Leftrightarrow\sqrt{2x+3}\left(\sqrt{2x-3}-2\right)=0\)

=>2x+3=0 hoặc 2x-3=4

=>x=7/2 hoặc x=-3/2

e: \(\Leftrightarrow\sqrt{x-2}\left(1-3\sqrt{x+2}\right)=0\)

=>x-2=0 hoặc 3 căn x+2=1

=>x=2 hoặc x+2=1/9

=>x=-17/9 hoặc x=2

4 nghiệm
-1; 2; 3; 6

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