Ta có \(\frac{\tan x}{1-\tan^2x}=\frac{\cot\left(x+\frac{\pi}{4}\right)}{2}\)

ĐKXĐ: \(\left\{{}\begin{matrix}cosx\ne0\\sin\left(x+\frac{\pi}{4}\right)\ne0\\cos\left(x+\frac{\pi}{4}\right)\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{2}+k\pi\\x\ne k\pi-\frac{\pi}{4}\end{matrix}\right.\)

\(\Leftrightarrow2\cdot\frac{sinx.cos^2x}{cosx.\left(cos^2x-sin^2x\right)}=\frac{sinx+cosx}{cosx-sinx}\)

\(\Leftrightarrow2sinx.cosx=\left(sinx+cosx\right)^2=1+2sinx.cosx\)

=> PTVN

Ta co: \(f\left(x\right)=2-\dfrac{3}{x+1}\)

Suy ra

\(A=\dfrac{f\left(x2\right)-f\left(x1\right)}{x2-x1}=\dfrac{\dfrac{3}{x2+1}-\dfrac{3}{x1+1}}{x2-x1}=\dfrac{3\dfrac{x1-x2}{\left(x1+1\right)\left(x2+1\right)}}{x2-x1}\)

\(=-\dfrac{3}{\left(x1+1\right)\left(x2+1\right)}\)

Vi xet ham so tren \(\left(-\infty;-1\right)\)

Nen \(\left(x1+1\right)\left(x2+1\right)>0\)

\(\Rightarrow A< 0\) suy ra ham so nghich bien

Theo de bai ta co: \(x=\dfrac{y^2}{z}\Rightarrow\dfrac{z}{x}=\dfrac{z^2}{y^2}\left(1\right)\)

Va \(y=\dfrac{z^2}{x}\left(2\right)\)

Tu (1),(2) suy ra y=z \(\Rightarrow x=y=z\)

suy ra A=1

USES crt;

VAR i:byte; s:integer;

Function kt(x:byte):boolean;

Var i:byte;

Begin

kt:=true;

if (x mod 2=0) or (x mod 3=0) then

begin

kt:=false;

exit;

end;

for i:=2 to trunc(sqrt(x)) do

if x mod i=0 then

begin

kt:=false;

exit;

end;

End;

BEGIN

clrscr;

writeln('Cac so nguyen to co 2 chu so gom:');

s:=0;

for i:=10 to 99 do

if kt(i) then

begin

write(i:4);

s:=s+i;

end;

readln;

END.

USES crt;

VAR s,n,i:integer;

BEGIN

clrscr;

write('Nhap n:');readln(n);

s:=0;

for i:=1 to n do

s:=s+sqr(i);

writeln('Ke qua cua s la:',sqrt(s));

readln;

END.

USES crt;

VAR i,n:integer;

BEGIN

clrscr;

write('Nhap n:');readln(n);

i:=1;

while i<=10 do

begin

writeln(n,' X ',i,'=',n*i);

inc(i);

end;

readln;

END.

USES crt;

VAR n:longint; i:byte;s:string;

BEGIN

clrscr;

write('Nhap n:');readln(n);

str(n,s);

writeln('Cac chu so cua ',n,' la:');

for i:=1 to length(s) do

write(s[i]:4);

readln;

END.