Question 93

If a - b = 3 and ab =28, then $$a^3 - b^3$$ is

Solution

Equation 1 : $$a - b = 3$$

=> $$a = 3 + b$$

Equation 2 : $$a \times b = 28$$

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

=> $$(3 + b) b = 28$$

=> $$3b + b^2 = 28$$

=> $$b^2 + 3b - 28 = 0$$

=> $$b^2 - 4b + 7b - 28 = 0$$

=> $$b(b - 4) + 7(b - 4) = 0$$

=> $$(b - 4) (b + 7) = 0$$

=> $$b = 4 , -7$$

=> $$a = 7 , -4$$

$$\therefore a^3 - b^3 = (7)^3 - (4)^3$$ (or) $$(-4)^3 - (-7)^3$$

= $$343 - 64 = 279$$

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If a -­ b = 3 and ab =28, then $$a^3 - b^3$$ is