program tinhp;

uses crt;

var x,n,i: integer;

s: real;

begin

write('Nhap n:');

readln(n);

write('Nhap x:');

readln(x);

s: sqrt(x);

for i:=1 to do s:= sqrt (x+s);

write('tong s=',s:6:2);

readln;

end.

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

=> \(\sqrt{x+\frac{1+\sqrt{4x+1}}{2}}=\sqrt{\left(\frac{1+\sqrt{4x+1}}{2}\right)^2}=\frac{1+\sqrt{4x+1}}{2}\). tiếp tục n dấu căn

=> A = \(\frac{1+\sqrt{4x+1}}{2}\) 

Biểu thức cần rút gọn : \(\sqrt{x+\sqrt{x+...+\sqrt{x+\frac{1+\sqrt{4x+1}}{2}}}}\) (ĐK : \(x\ge-\frac{1}{4}\))

Ta xét : \(x+\frac{1+\sqrt{4x+1}}{2}=\frac{2x+1+\sqrt{4x+1}}{2}=\frac{4x+1+2\sqrt{4x+1}+1}{4}=\left(\frac{\sqrt{4x+1}+1}{2}\right)^2\)

\(\Rightarrow\sqrt{x+\frac{1+\sqrt{4x+1}}{2}}=\frac{\sqrt{4x+1}+1}{2}\)

Do đó, biểu thức cần rút gọn sẽ bằng với : \(\frac{\sqrt{4x+1}+1}{2}\)

a: ĐKXĐ: 2x-10>=0

=>2x>=10

=>x>=5

b: \(\sqrt{A^2B}=\sqrt{A^2}\cdot\sqrt{B}=\left|A\right|\cdot\sqrt{B}\)

\(\sqrt{72}=\sqrt{36\cdot2}=6\sqrt{2}\)

c: \(A=\sqrt{16}+\sqrt{81}=4+9=13\)

\(B=\sqrt{\dfrac{\left(15\sqrt{5}+5\sqrt{200}-3\sqrt{450}\right)}{\sqrt{10}}}\)

\(=\sqrt{\dfrac{15}{\sqrt{2}}+5\sqrt{20}-3\sqrt{45}}\)

\(=\sqrt{\dfrac{15\sqrt{2}+2\sqrt{5}}{2}}=\sqrt{\dfrac{30\sqrt{2}+4\sqrt{5}}{4}}\)

\(=\dfrac{\sqrt{30\sqrt{2}+4\sqrt{5}}}{2}\)

\(C=\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{1+\sqrt{2}}-\left(2+\sqrt{3}\right)\)

\(=\dfrac{\sqrt{3}\left(2+\sqrt{3}\right)}{\sqrt{3}}-\left(2+\sqrt{3}\right)+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}\)

\(=2+\sqrt{3}-2-\sqrt{3}+\sqrt{2}=\sqrt{2}\)

\(1,ĐKXĐ:x\ge0\\ x\sqrt{3}=-\sqrt{3x^2}\\ \Leftrightarrow3x^2=9x^2\\ \Leftrightarrow6x^2=0\\ \Leftrightarrow x=0\left(tm\right)\)

\(2,ab^2\sqrt{a}=ab^2\sqrt{a}\)

\(3,a\sqrt{\dfrac{b}{a}}=\sqrt{ab}\)

\(ab^2\sqrt{a}=\sqrt{a^3b^4}\)

Câu 2: 

2) Ta có: \(M=\dfrac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}\)

\(=\dfrac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{2\sqrt{x}-9-x+9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{-\sqrt{x}}{\sqrt{x}-3}\)

Câu 2 : 

Gọi : vận tốc của người đi chậm là : x (km/h) ( x > 0 ) 

Vận tốc của người đi nhanh : x + 4 (km/h) 

Vi : người đi chậm đến muộn hơn : 45 phút \(=\dfrac{3}{4}\left(h\right)\)

Khi đó : 

\(\dfrac{36}{x}-\dfrac{36}{x+4}=\dfrac{3}{4}\)

\(\Leftrightarrow\left[36\cdot\left(x+4\right)-36x\right]\cdot4=3x\cdot\left(x+4\right)\)

\(\Leftrightarrow3x^2+12x-144=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=12\left(n\right)\\x=16\left(l\right)\end{matrix}\right.\)

Câu 1: 

1) Thay x=16 vào N, ta được:

\(N=\dfrac{2\cdot\sqrt{16}+1}{3-\sqrt{16}}=\dfrac{2\cdot4+1}{3-4}=\dfrac{9}{-1}=-9\)

Vậy: Khi x=16 thì N=-9

program Lam_Lui;

var S:extended;

i,n:integer;

begin

clrscr;

write('Nhap n = ');

readln(n);

S:=0;

for i:=n downto 1 do S:=sqrt(i+S);

write('Sai tự chịu: ',S);

readln;

end.

program Lam_Lui;

var S:extended;

i,n:integer;

begin

clrscr;

write('Nhap n = ');

readln(n);

S:=0;

for i:=n downto 1 do S:=sqrt(i+S);

writeln('Sai tự chịu: ',S);

readln;

end.

Trong MSWLOGO:

To tinhtoan :n
CS
make "A 0
FOR [i :n 1 -1][Make "A :A+sqrt(:i+:A)]
RT 90 LABEL (List "Tong "la: :A)
end

Mọi thắc mắc xin gửi về tổng đài: 1900, 1 ko ko có