Question

The function f(x)=g(x), where f(x)=2x-5 and g(x)=x^2-6. The table below shows the process of solving using successive approximations. Continue this process to find the positive solution to the nearest 10th.

Answer 1

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 $f(x)=2x-5$ and $g(x)=x^2-6$

To find : The positive solution of the given situation.

Solution :

We have given the functions :

$f(x)=2x-5$ and $g(x)=x^2-6$

The condition is f(x)=g(x)

Substitute the values, in the given condition

$f(x)=g(x)$

$2x-5=x^2-6$

$x^2-2x-1=0$

Solving the quadratic equation by discriminant method,

General form - $ax^2+bx+c=0$

$D=b^2-4ac$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

Equation is $x^2-2x-1=0$

where a=1 , b=-2, c=-1

$D=b^2-4ac$

$D=(-2)^2-4(1)(-1)$

$D=4+4$

$D=8$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-(-2)\pm\sqrt{8}}{2(1)}$

$x=\frac{2\pm2\sqrt{2}}{2}$

$x=1\pm\sqrt{2}$

$x=1+\sqrt{2}, x=1-\sqrt{2}$

$x=2.4, x=-0.4$

Therefore, The solutions of the given situation is x=2.4 and x=-0.4.

Answer 2

Answer:

The positive solution is 2.4.

Step-by-step explanation:

The given functions are

$f(x)=2x-5$

$g(x)=x^2-6$

It is given that

$f(x)=g(x)$

$2x-5=x^2-6$

$0=x^2-6-2x+5$

$0=x^2-2x-1$

The quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{2\pm \sqrt{(2)^2-4(1)(-1)}}{2(1)}$

$x=\frac{2\pm \sqrt{8}}{2}$

$x=\frac{2\pm 2\sqrt{2}}{2}$

$x=\frac{2(1\pm \sqrt{2})}{2}$

$x=1\pm \sqrt{2}$

$x=2.4,-0.4$

Therefore the positive solution is 2.4.