Question 43

If a + b = 10 and ab = 24, then the value of $$a^3 + b^3$$ is

Solution

Equation 1 : $$a + b = 10$$

=> $$a = 10 - b$$

Equation 2 : $$a \times b = 24$$

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

=> $$(10 - b) b = 24$$

=> $$10b - b^2 = 24$$

=> $$b^2 - 10b + 24 = 0$$

=> $$b^2 - 4b - 6b + 24 = 0$$

=> $$b(b - 4) - 6(b - 4) = 0$$

=> $$(b - 4) (b - 6) = 0$$

=> $$b = 4 , 6$$

=> $$a = 6 , 4$$

$$\therefore a^3 + b^3 = (4)^3 + (6)^3$$

= $$64 + 216 = 280$$

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