\(\dfrac{62.63+75}{12+62.64}=\dfrac{62.63+63+12}{12+62.64}=\dfrac{62.64+12}{12+62.64}=1\)

\(\dfrac{62\times63+75}{12+62\times64}=\dfrac{62\times\left(64-1\right)+63+12}{12+62\times64}=\dfrac{62\times64-62+63+12}{12+62\times64}=\dfrac{62\times64+1+12}{12+62\times64}=1\)

+ Hình 62:

• ∆ABC có AC = AB ⟹ ∆ABC cân tại A 

• ∆ABC vuông tại A  (trong tam giác vuông, hai góc nhọn phụ nhau) hay

+ Hình 63: Vẽ tia Ct // BA ( tia BA và tia Ct thuộc hai nửa mặt phẳng đối nhau có bờ BC)

+ Hình 64:

Câu 1=2

Câu 2=0

tick cái nha

63x(64-62)+62x(62-64)

=63x2+62x2

=(63+62)x2

=125x2

=250

a:=2

b:=0

a) Ta có: \(\left(x-1\right)^{x+2}-\left(x-1\right)^{x+4}=0\)

\(\Leftrightarrow\left(x-1\right)^x\cdot\left(x-1\right)^2-\left(x-1\right)^x\cdot\left(x-1\right)^4=0\)

\(\Leftrightarrow\left(x-1\right)^{x+2}\cdot\left[1-\left(x-1\right)^2\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-1=1\\x-1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=0\end{matrix}\right.\)

b) Ta có: \(\dfrac{1}{4}\cdot\dfrac{2}{6}\cdot\dfrac{3}{8}\cdot\dfrac{4}{10}\cdot\dfrac{5}{15}\cdot...\cdot\dfrac{30}{62}\cdot\dfrac{31}{64}=2x\)

\(\Leftrightarrow2x=\dfrac{1}{64}\)

hay \(x=\dfrac{1}{128}\)

Ta có: \(2^x=\dfrac{1}{4}\cdot\dfrac{2}{6}\cdot\dfrac{3}{8}\cdot\dfrac{4}{10}\cdot\dfrac{5}{12}\cdot...\cdot\dfrac{30}{62}\cdot\dfrac{31}{64}\)

\(\Leftrightarrow2^x=\dfrac{1\cdot2\cdot3\cdot4\cdot...\cdot31}{2\cdot\left(2\cdot3\cdot4\cdot...\cdot31\right)\cdot64}\)

\(\Leftrightarrow2^x=\dfrac{1}{2}\cdot\dfrac{1}{64}=\dfrac{1}{128}\)
\(\Leftrightarrow2^x=\dfrac{1}{2^6}\)

\(\Leftrightarrow2^{x+6}=1\)

\(\Leftrightarrow x+6=0\)

hay x=-6

Vậy: x=-6

`1/4 . 2/6 . 3/8 ... . 30/62 .31/64 =2^x`

`-> (1.2.3....30.31)/(4.6.8....62.64)=2^x`

`-> (1.(2.3...31))/(2.(2.3.4...31).32)=2^x`

`-> 1/(2.32)=2^x`

`-> 1/64=2^x`

`-> 1/(2^6)=2^x`

`-> x=-6`.

\(-62.\left(27-64\right)-64.\left(62-27\right)\)

\(=\left(-67\right).27+62.64-\left(-64\right).62+64.27\)

\(=\left(-67\right).27+64.27+62.24+64.62\)

\(=27.\left(-67+64\right)+62.\left(24+64\right)\)

\(=27.\left(-3\right)+62.88\)

\(=-81+5456\)

\(=5375\)

Có: \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}=\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}...\frac{30}{2.31}.\frac{31}{2.32}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}...\frac{1}{2}.\frac{1}{2}.\frac{1}{32}\)

\(=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}=2^x\)\(\Rightarrow1=2^x.2^{36}=2^{36+x}\)\(\Rightarrow2^{36+x}=2^0\Rightarrow36+x=0\Rightarrow x=-36\)