\(K=\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+...}}}}\)

Nhận xét : K > 0

Bình phương hai vế : \(K^2-5=\sqrt{13+\sqrt{5+\sqrt{13+...}}}\)

\(\Leftrightarrow\left(K^2-5\right)^2-13=K\)

\(\Leftrightarrow K^4-10K^2-K+12=0\)

\(\Leftrightarrow\left(K-3\right)\left(K^3+3K^2-K-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}K-3=0\left(1\right)\\K^3+3K^2-K-4=0\left(2\right)\end{cases}}\)

Tới đây bạn giải được rồi nhé! (chú ý rẳng K > 0)

Chiều rộng : 7,5 - 2,75 = 4,75 m

Chiều dài sau khi kéo dài : 7,5 + 2,5 = 10 m

DT ADMN : 10 x 4,75 = 475 m²

kết quả 1999

1+1+9+9+9+100

=129

K MK NHA

1 + 2 + 3 + 4 =10

200 con,không hiểu thì cứ hỏi mik

a. \(\frac{x-5}{100}+\frac{x-4}{101}+\frac{x-3}{102}=\frac{x-100}{5}+\frac{x-101}{4}+\frac{x-102}{3}\)

\(\Rightarrow\frac{x-5}{100}-1+\frac{x-4}{101}-1+\frac{x-3}{102}-1=\frac{x-100}{5}-1+\frac{x-101}{4}-1+\frac{x-102}{3}-1\)

\(\Rightarrow\frac{x-105}{100}+\frac{x-105}{101}+\frac{x-105}{102}-\frac{x-105}{5}-\frac{x-105}{4}-\frac{x-105}{3}=0\)

\(\Rightarrow\left(x-105\right)\left(\frac{1}{100}+\frac{1}{101}+\frac{1}{102}-\frac{1}{5}-\frac{1}{4}-\frac{1}{3}\right)=0\)

\(\Rightarrow x-105=0\left(\frac{1}{100}+\frac{1}{101}+\frac{1}{102}-\frac{1}{5}-\frac{1}{4}-\frac{1}{3}\ne0\right)\)

\(\Rightarrow x=105\)

b. \(\frac{29-x}{21}+\frac{27-x}{23}+\frac{25-x}{25}+\frac{23-x}{27}+\frac{21-x}{29}=-5\)

\(\Rightarrow\frac{29-x}{21}+1+\frac{27-x}{23}+1+\frac{25-x}{25}+1+\frac{23-x}{27}+1+\frac{21-x}{29}+1=0\)

\(\Rightarrow\frac{50-x}{21}+\frac{50-x}{23}+\frac{50-x}{25}+\frac{50-x}{27}+\frac{50-x}{29}=0\)

\(\Rightarrow\left(50-x\right)\left(\frac{1}{21}+\frac{1}{23}+\frac{1}{25}+\frac{1}{27}+\frac{1}{29}\right)=0\)

\(\Rightarrow50-x=0\left(\frac{1}{21}+\frac{1}{23}+\frac{1}{25}+\frac{1}{27}+\frac{1}{29}\ne0\right)\)

\(\Rightarrow x=50\)

vẽ sơ đồ