The equations are approximately equals to the points (0.618 , 4.236) and (-1.618 , -0.236)
What is a factorization?
'Factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number.'
According to the given problem,
y = x² + 3x + 2 .... equation 1
y = 2x + 3 .... equation 2
For solving the system of equations, we have to equate equation 1 and equation 2,
x² + 3x + 2 = 2x + 3
⇒ x² + 3x - 2x + 2 - 3 = 0
⇒ x² + x - 1 = 0
The formula to solve a quadratic equation of the form ax² + bx + c equal to x = [tex]\frac{-b (+/-)\sqrt{b^{2} - 4ac } }{2a}[/tex]
In this problem,
x² + x - 1 = 0
so, a = 1 , b = 1 , c = -1
x = 0.618 , - 1.618 [ after putting the values and solving for x ]
for, x = -1.618
y = 2(-1.618) + 3
⇒ y = -0.236
For x = 0.618
y = 2(0.618) + 3
⇒ y = 4.236
Hence, we can conclude that the equations are approximately equal to the point (0.618, 4.236) and (-1.618 , -0.236).
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