Help - Pt of Intersection (1 Viewer)

[withyou]

Of the curves:

y=x^3 and y=-3x+4

With explanation with each step, ty:uhhuh:

 

[tommykins]

x^3 = -3x + 4
x^3 + 3x - 4 = 0
testing in factors of 4, 1 is a solution.

(1)^3 + 3(1) - 4 = 0
1 +3 -4 = 0

thus x =1 is the point of intersection.

 

[Trebla]

(1,1) is the POINT of interesection, not x = 1...
x³ + 3x - 4 = 0
x³ - 1 + 3x - 3 = 0
(x - 1)(x² + x + 1) + 3(x - 1) = 0
(x - 1)(x² + x + 4) = 0
x = 1, sub into y = x³
y = 1

 

[Arkie]

they equal each other because
they both equal y
if u didnt pick up on that so he subed one into the other
and to find the co ordinante of y
sub 1 into the equation

 

[tommykins]

(1,1) is the POINT of interesection, not x = 1...
x³ + 3x - 4 = 0
x³ - 1 + 3x - 3 = 0
(x - 1)(x² + x + 1) + 3(x - 1) = 0
(x - 1)(x² + x + 4) = 0
x = 1, sub into y = x³
y = 1

ahah ty