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