Answer:
The solutions of the given situation is x=2.4 and x=-0.4.
Step-by-step explanation:
Given : The function f(x)=g(x), where [tex]f(x)=2x-5[/tex] and [tex]g(x)=x^2-6[/tex]
To find : The positive solution of the given situation.
Solution :
We have given the functions :
[tex]f(x)=2x-5[/tex] and [tex]g(x)=x^2-6[/tex]
The condition is f(x)=g(x)
Substitute the values, in the given condition
[tex]f(x)=g(x)[/tex]
[tex]2x-5=x^2-6[/tex]
[tex]x^2-2x-1=0[/tex]
Solving the quadratic equation by discriminant method,
General form - [tex]ax^2+bx+c=0[/tex]
[tex]D=b^2-4ac[/tex]
Solution is [tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
Equation is [tex]x^2-2x-1=0[/tex]
where a=1 , b=-2, c=-1
[tex]D=b^2-4ac[/tex]
[tex]D=(-2)^2-4(1)(-1)[/tex]
[tex]D=4+4[/tex]
[tex]D=8[/tex]
Solution is [tex]x=\frac{-b\pm\sqrt{D}}{2a}[/tex]
[tex]x=\frac{-(-2)\pm\sqrt{8}}{2(1)}[/tex]
[tex]x=\frac{2\pm2\sqrt{2}}{2}[/tex]
[tex]x=1\pm\sqrt{2}[/tex]
[tex]x=1+\sqrt{2}, x=1-\sqrt{2}[/tex]
[tex]x=2.4, x=-0.4[/tex]
Therefore, The solutions of the given situation is x=2.4 and x=-0.4.
