Lời giải:
a.

Nếu $m=3$ thì pt trở thành:
$x^2+4x-5=0$

$\Leftrightarrow (x-1)(x+5)=0$

$\Leftrightarrow x=1$ hoặc $x=-5$

b.

Để pt có 2 nghiệm pb $x_1,x_2$ thì:

$\Delta'=4+m^2-4>0\Leftrightarrow m^2>0\Leftrightarrow m\neq 0$

PT có 2 nghiệm $(-2+m, -2-m)$

Khi đó:

\(x_2=x_1^3+4x_2^2\Leftrightarrow \left[\begin{matrix} -2+m=(-2-m)^3+4(-2+m)^2\\ -2-m=(-2+m)^3+4(-2-m)^2\end{matrix}\right.\)

\(\Leftrightarrow \left[\begin{matrix} -m^3+2m^2-29m+10=0\\ m^3-2m^2+29m+10=0\end{matrix}\right.\)

Nghiệm khá xấu, cảm giác đề cứ sai sai bạn ạ.

#include <bits/stdc++.h>

using namespace std;

double a,b,c,p,s;

int main()

{

cin>>a>>b>>c;

p=(a+b+c)/2;

s=sqrt(p*(p-a)*(p-b)*(p-c));

cout<<fixed<<setprecision(2)<<p;

return 0;

}

1: 

uses crt;

var a,b,c,max,min:longint;

begin

clrscr;

readln(a,b,c);

max=a;

if max<b then max:=b;

if max<c then max:=c;

min:=a;

if min>c then min:=c;

if min>b then min:=b;

writeln(max,' ',min);

readln;

end.

Bài 1.2

\(A=\dfrac{2\sqrt{x}+7}{\sqrt{x}+2}=2+\dfrac{3}{\sqrt{x}+2}\)

C1:Bạn dùng pp chặn như bài 2.2

C2: (Gợi ý)\(\sqrt{x}+2\ge2\) và \(\sqrt{x}+2\inƯ\left(3\right)\)\(\Rightarrow\sqrt{x}+2=3\Leftrightarrow x=1\)

Vậy x=1 thì A nguyên

Bài 2.2

\(A=\dfrac{\sqrt{x}+7}{\sqrt{x}+2}=1+\dfrac{5}{\sqrt{x}+2}\)

Do \(\sqrt{x}\ge0;\forall x\)\(\Rightarrow\sqrt{x}+2\ge2\) \(\Rightarrow\dfrac{5}{\sqrt{x}+2}\le\dfrac{5}{2}\)\(\Rightarrow A\le\dfrac{7}{2}\) (1)

mà \(\dfrac{5}{\sqrt{x}+2}>0;\forall x\Rightarrow A>1\) (2)

Từ (1) (2) \(\Rightarrow1< A\le\dfrac{7}{2}\) mà A nguyên

\(\Rightarrow\left[{}\begin{matrix}A=2\\A=3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}1+\dfrac{5}{\sqrt{x}+2}=2\\1+\dfrac{5}{\sqrt{x}+2}=3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}+2=5\\\sqrt{x}+2=\dfrac{5}{2}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\\\sqrt{x}=\dfrac{1}{2}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=9\\x=\dfrac{1}{4}\end{matrix}\right.\)

Vậy...

Bài 3.2

\(A=\dfrac{-x-2\sqrt{x}-5}{\sqrt{x}+2}\)\(=\dfrac{-\sqrt{x}\left(\sqrt{x}+2\right)-5}{\sqrt{x}+2}=-\sqrt{x}-\dfrac{5}{\sqrt{x}+2}\)

\(=2-\left(\sqrt{x}+2+\dfrac{5}{\sqrt{x}+2}\right)\)

Áp dụng bđt cosi: \(\sqrt{x}+2+\dfrac{5}{\sqrt{x}+2}\ge2\sqrt{\left(\sqrt{x}+2\right).\dfrac{5}{\sqrt{x}+2}}=2\sqrt{5}\)

\(\Rightarrow A\le2-2\sqrt{5}\)

Dấu = xảy ra \(\Leftrightarrow\sqrt{x}+2=\dfrac{5}{\sqrt{x}+2}\Leftrightarrow x=9-4\sqrt{5}\)