Ex14.mw

> Exercice 14

> restart;

> Equation:=abs(x-3)+abs(x+4)<=7;Solution=solve(Equation,x);

Equation := abs(x-3)+abs(x+4) <= 7

Solution = RealRange(-4, 3)

> Equation1:=0<=x/(x^2-1);Equation2:=x/(x^2-1)<=1;sol1:=solve(Equation1,x);sol2:=solve(Equation2,x);

Equation1 := 0 <= x/(x^2-1)

Equation2 := x/(x^2-1) <= 1

sol1 := RealRange(Open(-1), 0), RealRange(Open(1), infinity)

sol2 := RealRange(-infinity, Open(-1)), RealRange(1/2-1/2*5^(1/2), Open(1)), RealRange(1/2+1/2*5^(1/2), infinity)

> Equation:=(x^3-1)/(x+1)<=x^2-x-1;Solution=solve(Equation,x);

Equation := (x^3-1)/(x+1) <= -x+x^2-1

Solution = RealRange(Open(-1), 0)

> Equation1:=sqrt(x**2+3)-sqrt(x**2+1)<=1;Solution1=solve(Equation1,x);Equation1:=sqrt(x**2+3)-sqrt(x**2+1)>=0;Solution1=solve(Equation2,x);

Equation1 := (x^2+3)^(1/2)-(x^2+1)^(1/2) <= 1

Solution1 = x

Equation1 := 0 <= (x^2+3)^(1/2)-(x^2+1)^(1/2)

Solution1 = (RealRange(-infinity, Open(-1)), RealRange(1/2-1/2*5^(1/2), Open(1)), RealRange(1/2+1/2*5^(1/2), infinity))

> Equation:=sqrt(x**2-4*x+4)>=abs(3*x/2-1);Solution=solve(Equation,x);

Equation := abs(3/2*x-1) <= ((-2+x)^2)^(1/2)

Solution = RealRange(-2, 6/5)