Question 96

Two fractions are such that their product is 2/5 and sum is 19/15. What are the two fractions.

Solution

Let the two numbers be x and y

=> $$x + y = \frac{19}{15}$$ and $$x.y = \frac{2}{5}$$

=> $$x(\frac{19}{15} - x) = \frac{2}{5}$$

=> $$x(\frac{19 - 15x}{15}) = \frac{2}{5}$$

=> $$19x - 15x^2 = 6$$

=> $$15x^2 - 19x + 6 = 0$$

=> $$15x^2 - 10x - 9x + 6 = 0$$

=> $$5x(3x - 2) - 3(3x - 2) = 0$$

=> $$(5x - 3) (3x - 2) = 0$$

=> $$x = \frac{3}{5} , \frac{2}{3}$$

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Two fractions are such that their product is ­2/5 and sum is 19/15. What are the two fractions.