Question 55

The sum of two numbers is 24 and their product is 143. The sum of their squares is

Solution

Let the number be $$x$$ and $$(24 - x)$$

=> Product = $$x (24 - x) = 143$$

=> $$x^2 - 24x + 143 = 0$$

=> $$(x - 13) (x - 11) = 0$$

=> $$x = 13 , 11$$

Other number = $$11 , 13$$

Thus, the two numbers are = 11 and 13

$$\therefore$$ Sum of their squares = $$(11)^2 + (13)^2$$

= $$121 + 169 = 290$$

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