Question

At which points are the equations y = x2 + 5x − 2 and y = x + 1 equal?

Answer 1

`x^2+5x-2=x+1\\ x^2+4x-3=0\\ x^2+4x+4-7=0\\ (x+2)^2=7\\ x+2=-\sqrt7 \vee x+2=\sqrt7\\ x=-2-\sqrt7 \vee x=-2+\sqrt7`

Answer 2

common points will be [(-2+√7), (-1 + √7)] and [(-2-√7), (-1 -√7)]

Explanation:

we have to find the point at which the equations are equal.

y = x² + 5x - 2 and y = x + 1

Now we Equate both the equations the point of intersections of both the equations

x² + 5x - 2 = x + 1

x² + 5x - x - 2 = 1

x² + 4x = 1 + 2

x² + 4x = 3

x² + 4x + 4 = 3 + 4

(x + 2)² = 7

x + 2 = ±√7

x = -2 ± √7

Since y = x + 1

Therefore, y = (-2 ± √7) + 1

y = -1 ± √7

Therefore, common points will be [(-2+√7), (-1 + √7)] and [(-2-√7), (-1 -√7)]