Final answer:
To find a³-b³ when a-b=5 and ab=-4, we can use the identity a³ - b³ = (a-b)(a²+ab+b²). Solve for a and b using the given equations, substitute the values into the formula, and calculate the result.
Step-by-step explanation:
To find a³-b³ when a-b=5 and ab=-4, we can use the identity a³ - b³ = (a-b)(a²+ab+b²). Let's solve for a and b using the given equations.
From a-b=5, we can rearrange to get a = b+5. Substituting this into ab=-4, we have (b+5)b=-4.
Simplifying, we get b²+5b+4=0. Factoring or using the quadratic formula, we find that b = -1 or b = -4. Plugging these values into a = b+5, we get a = 4 or a = 1.
Now, substituting the values of a and b into a³ - b³ = (a-b)(a²+ab+b²), we find that a³ - b³ = (4-(-1))((4)²+(4)(-1)+(-1)²) = 15(13) = 195.