Question 79

If a - b = 6 and ab =16, then $$a^3 - b^3$$ is

Solution

Equation 1 : $$a - b = 6$$

=> $$a = 6 + b$$

Equation 2 : $$a \times b = 16$$

Substituting value of 'a' in equation 2, we get :

=> $$(6 + b) b = 16$$

=> $$6b + b^2 = 16$$

=> $$b^2 + 6b - 16 = 0$$

=> $$b^2 - 2b + 8b - 16 = 0$$

=> $$b(b - 2) + 8(b - 2) = 0$$

=> $$(b - 2) (b + 8) = 0$$

=> $$b = 2 , -8$$

=> $$a = 8 , -2$$

$$\therefore a^3 - b^3 = (8)^3 - (2)^3$$ (or) $$(-2)^3 - (-8)^3$$

= $$512 - 8 = 504$$

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If a -­ b = 6 and ab =16, then $$a^3 - b^3$$ is