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

Question

Need help ASAP. Advanced Algebra

Answer 1

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

Answer 2

Multiplying first eqn through by y: xy+1=7y/2; and second eqn by x: xy+1=7x/5. Therefore xy=7y/2-1=7x/5-1.

y/2=x/5 and y=2x/5. Or, xy+1=7y/2=7x/5, and y=2x/5. So substituting for y in 2nd eqn: 2x^2/5+1=7x/5, 2x^2-7x+5=0=(2x-5)(x-1)=0, x=1 or 5/2.

So y is 2/5 or 1 and xy=2/5 or 5/2=0.4 or 2.5; the maximum is 2.5.