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3 years ago

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

Mathematics

2 answers:

RoseWind [281]3 years ago

6 0

Answer:

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

Step-by-step 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)]

Margaret [11]3 years ago

4 0

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

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