Two fractions are such that their product is 9/10 and sum is 77/40. What are the two fractions.
Let the two numbers be x and y
=> $$x + y = \frac{77}{40}$$ and $$x.y = \frac{9}{10}$$
=> $$x(\frac{77}{40} - x) = \frac{9}{10}$$
=> $$x(\frac{77 - 40x}{40}) = \frac{9}{10}$$
=> $$77x - 40x^2 = 36$$
=> $$40x^2 - 77x + 36 = 0$$
=> $$40x^2 - 32x - 45x + 36 = 0$$
=> $$8x(5x - 4) - 9(5x - 4) = 0$$
=> $$(8x - 9) (5x - 4) = 0$$
=> $$x = \frac{9}{8} , \frac{4}{5}$$
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