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

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Answer:


a^3+b^3=0Step-by-step 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

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