Ta có: \(AB^2+HC^2=\left(AA'^2+A'B^2\right)+\left(A'H^2+A'C^2\right)\)

\(=\left(AA'^2+A'C^2\right)+\left(A'B^2+A'H^2\right)=AC^2+HB^2\)

Lại có: \(BC^2+HA^2=\left(BB'^2+B'C^2\right)+\left(B'H^2+B'A^2\right)\)

\(=\left(BB'^2+B'A^2\right)+\left(B'C^2+B'H^2\right)=AB^2+HC^2\)

\(\Rightarrow AB^2+HC^2=AC^2+HB^2=BC^2+HA^2\)

1.A

2.C

3.C

4.B

5.A

1. A

2. C

3. C

4. B

5. A

b: Ta có: \(\dfrac{3x-1}{2}=\dfrac{2x-2}{3}\)

\(\Leftrightarrow9x-3=4x-4\)

\(\Leftrightarrow x=-\dfrac{1}{5}\)

\(a,\Leftrightarrow\dfrac{2}{3}\left(3x-2\right)+\dfrac{4}{9}\left(3x-5\right)=-2x+1\\ \Leftrightarrow2x-\dfrac{4}{3}+\dfrac{4}{3}x-\dfrac{20}{9}+2x-1=0\\ \Leftrightarrow\dfrac{16}{3}x=\dfrac{41}{9}\Leftrightarrow x=\dfrac{41}{9}\cdot\dfrac{3}{16}=\dfrac{41}{48}\\ b,\Leftrightarrow3\left(3x-1\right)=2\left(2x-2\right)\\ \Leftrightarrow9x-3=4x-4\\ \Leftrightarrow5x=-1\Leftrightarrow x=-\dfrac{1}{5}\\ c,\Leftrightarrow15-2\left(x^2+1\right)=7\\ \Leftrightarrow13-2x^2=7\Leftrightarrow x^2=3\Leftrightarrow x=\pm\sqrt{3}\)

\(d,\Leftrightarrow x+1=\sqrt{x+1}\left(x\ge-1\right)\\ \Leftrightarrow x^2+2x+1=x+1\\ \Leftrightarrow x^2-x=0\\ \Leftrightarrow x\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=1\left(tm\right)\end{matrix}\right.\)

120 dm² x 5 + 4m² = 600 dm² +  4 m² = 6 m² + 4m² = 10 m²