Question 75

If $$a^3 - b^3 = 899 and a - b = 29, then (a - b)^2 + 3ab$$ is equal to:

Solution

As we know the identity :

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

$$\therefore 899 = 29 * (a^2 + ab + b^2)$$

$$\therefore (a^2 + ab + b^2) = 899\div29$$

So $$(a^2 + ab + b^2 ) = 31$$

$$\Rightarrow(a^2 + ab + b^2 - 2ab + 2ab)= 31$$

$$\Rightarrow(a - b)^2 + 3ab = 31$$

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