Question

At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?

Answer 1

Use a system:

$2x+3=x^2+3x+2$

$0=x^2+x-1$

$x=0.618$

$x=-1.618$

Answer 2

Answer:

The equations are approximately equals at the points $(0.618,4.236)$ and $(-1.618,-0.236)$

Step-by-step explanation:

we have

$y=x^{2}+3x+2$ -----> equation A

$y=2x+3$ -----> equation B

To solve the system of equations equate equation A to equation B

$x^{2}+3x+2=2x+3$

Group terms that contain the same variable

$x^{2}+3x-2x+2-3=0$

$x^{2}+x-1=0$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}+x-1=0$

so

$a=1\\b=1\\c=-1$

substitute in the formula

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

$x=\frac{-1(+/-)\sqrt{5}} {2}$

$x=\frac{-1+\sqrt{5}}{2}=0.618$

$x=\frac{-1-\sqrt{5}}{2}=-1.618$

Find the values of y

For $x=0.618$

$y=2(0.618)+3=4.236$

For $x=-1.618$

$y=2(-1.618)+3=-0.236$

Therefore

The equations are approximately equals at the points $(0.618,4.236)$ and $(-1.618,-0.236)$