Sure, let's prove the equation step by step.

We know that the formula for a^3 + b^3 + c^3 - 3abc is equal to (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

Given that a + b + c = 5 and ab + bc + ca = 10, we can substitute these values into the formula.

So, a^3 + b^3 + c^3 - 3abc = (5)(a^2 + b^2 + c^2 - 10)

We also know that a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca) = 5^2 - 2*10 = 5

Substituting this value into the formula, we get:

a^3 + b^3 + c^3 - 3abc = (5)(5 - 10) = -25

Therefore, a^3 + b^3 + c^3 - 3abc = -25.

Question

Sure, let's prove the equation step by step.

We know that the formula for a^3 + b^3 + c^3 - 3abc is equal to (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

Given that a + b + c = 5 and ab + bc + ca = 10, we can substitute these values into the formula.

So, a^3 + b^3 + c^3 - 3abc = (5)(a^2 + b^2 + c^2 - 10)

We also know that a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + bc + ca) = 5^2 - 2*10 = 5

Substituting this value into the formula, we get:

a^3 + b^3 + c^3 - 3abc = (5)(5 - 10) = -25

Therefore, a^3 + b^3 + c^3 - 3abc = -25.

Knowee AI · Accepted Answer