Question

7-4) Find all possible values of a^3 + b^3 if a^2 + b^2 = ab = 4

Answer 1

Answer:

$a^3+b^3=0$Explanation:

The given expression is:

$a^3+b^3$

This can be expressed as:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

This can also be written as:

$a^3+b^3=(a+b)(a^2b_{}+b^2-ab)$

Since a² + b² = ab:

a² + b² - ab = 0

Therefore:

$\begin{gathered} a^3+b^3=(a+b)(0) \\ a^3+b^3=0 \end{gathered}$

The value of a³ + b³ if a² + b² = ab = 4 is 0