Two fractions are such that their product is 4 and sum is 68/15. Find the two fractions.
Let the two numbers be x and y
=> $$x + y = \frac{68}{15}$$ and $$x.y = 4$$
=> $$x(\frac{68}{15} - x) = 4$$
=> $$x(\frac{68 - 15x}{15}) = 4$$
=> $$68x - 15x^2 = 60$$
=> $$15x^2 - 68x + 60 = 0$$
=> $$15x^2 - 50x - 18x + 60 = 0$$
=> $$5x(3x - 10) - 6(3x - 10) = 0$$
=> $$(5x - 6) (3x - 10) = 0$$
=> $$x = \frac{6}{5} , \frac{10}{3}$$
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