Question

What is the maximum value of xy if x + 1/y = 7/2 and y + 1/x = 7/5? Express your answer as a decimal to the nearest tenth.

Answer 1

Step-by-step explanation:

Multiplying both given equations, (xy) + 1/(xy) = 29/10

Cross multiplying and rearranging, 10(xy)² - 29(xy) + 10 = 0

This is quadratic in (xy), whose graph is a parabola opening upwards. Hence it has only minimum defined value and maximum value is not defined.

Min defined value is the vertex of the parabola, which is given by (-b/2a, -D/4a).

-b/2a = 29/20

So evaluating with the function minimum value for xy = -11.25

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hope it's helps ✅⚡

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