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hình bé quá

sin 65⁰=cos 35⁰
\(cos70^0=sin30^0\)
\(tan80^0=cot20^0\)
\(cot68^0=tan32^0\)

Ko nhìn chữ bn ơi, bn cho to hình một tý

a.

Đặt \(\left\{{}\begin{matrix}\sqrt{x^2+2x+3}=a>0\\\sqrt{x^2+x+2}=b>0\end{matrix}\right.\) \(\Rightarrow a^2-b^2=x+1\)

Pt trở thành:

\(a+b=2\left(a^2-b^2\right)\)

\(\Leftrightarrow a+b=\left(2a-2b\right)\left(a+b\right)\)

\(\Leftrightarrow2a-2b=1\) (do \(a+b>0\))

\(\Leftrightarrow2a=2b+1\)

\(\Leftrightarrow2\sqrt{x^2+2x+3}=2\sqrt{x^2+x+2}+1\)

\(\Leftrightarrow4\left(x^2+2x+3\right)=4\left(x^2+x+2\right)+1+4\sqrt{x^2+x+2}\)

\(\Leftrightarrow4x+3=4\sqrt{x^2+x+2}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{3}{4}\\16\left(x^2+x+2\right)=\left(4x+3\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{3}{4}\\8x=23\end{matrix}\right.\) \(\Rightarrow x=\dfrac{23}{8}\)

b.

ĐKXĐ: \(x\ge3\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x-3}=a\ge0\\\sqrt{x+2}=b>0\end{matrix}\right.\) \(\Rightarrow a^2-b^2=-5\)

Phương trình trở thành:

\(\left(a-b\right)\left(ab+1\right)=a^2-b^2\)

\(\Leftrightarrow\left(a-b\right)\left(ab+1\right)=\left(a-b\right)\left(a+b\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}a=b\left(vô-nghiệm\right)\\ab+1=a+b\end{matrix}\right.\)

\(\Rightarrow ab-a-b+1=0\)

\(\Leftrightarrow\left(a-1\right)\left(b-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}a=1\\b=1\end{matrix}\right.\)

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

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-1\left(ktm\right)\end{matrix}\right.\)