Answer:
c - a = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Since the parabolas intersect we can equate them, that is
2x² - 1 = - x² - x + 1 ← subtract terms on right side from terms on left side
3x² + x - 2 = 0
Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 2 = - 6 and sum = + 1
The factors are + 3 and - 2
Use these factors to split the x- term
3x² + 3x - 2x - 2 = 0 ( factor the first/second and third/fourth terms )
3x(x + 1) - 2(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(3x - 2) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]
Since c > a, then
a = - 1 and c = [tex]\frac{2}{3}[/tex]
Thus
c - a = [tex]\frac{2}{3}[/tex] - (- 1) = [tex]\frac{2}{3}[/tex] + 1 = [tex]\frac{2}{3}[/tex] + [tex]\frac{3}{3}[/tex] = [tex]\frac{5}{3}[/tex]
