\(\Leftrightarrow\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x.\left(x+1\right)}\)=\(\dfrac{99}{100}\)

\(\Leftrightarrow\)\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\)=\(\dfrac{99}{100}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}\)=\(\dfrac{99}{100}\)

\(\Leftrightarrow\dfrac{1}{x+1}\)=\(\dfrac{1}{100}\)

\(\Leftrightarrow x+1\)=100

\(\Leftrightarrow\)\(x\)=99

Diện tích một viên gạch là: 10\(\times\)10=100(cm²)

Diện tích mảng tường là: 100\(\times\)9=900(cm²)

Đ/s: 900cm²

(2x-m)(x+1)-2x²-mx+m-4=0

\(\Leftrightarrow\)2x²+2x-mx-m-2x²-mx+m-4=0

\(\Leftrightarrow\)-2mx-4=0

\(\Leftrightarrow\)-2mx=4

Thay x=-1 vào phương trình, ta có:

-2m(-1)=4

\(\Leftrightarrow\)2m=4

\(\Leftrightarrow\)m=2

(2x-1)²=(\(\dfrac{1}{2}\)-x)²

^{\(\Leftrightarrow\)}4x²-4x+1=\(\dfrac{1}{4}\)-x+x²

^{\(\Leftrightarrow\)}3x²-3x+\(\dfrac{3}{4}\)=0

\(\Leftrightarrow\)3(x²-x+\(\dfrac{1}{4}\))=0

\(\Leftrightarrow\)(x-\(\dfrac{1}{2}\))²=0

\(\Leftrightarrow\)x-\(\dfrac{1}{2}\)=0

\(\Leftrightarrow\)x=\(\dfrac{1}{2}\)