The sum of two numbers is 48, and the sum of their reciprocals is 16. Find their product.

Answer 1

x + y=48, so x=48-y

1/x + 1/y = 16

and

1/(48-y) +1/y = 16

simplify

multiply both sides by (48-y)y

y + (48-y) = 16y(48-y)

48 = (16)(48)y-16y²

Divide by 16

3 = 48y-y²

rearrange to a standard quadratic equation, with decreasing powers of y

y² -48y + 3 = 0

If you can't factor, then use the quadratic formula or complete the square. Take half of 48 and square it. then add and subtract it on the left side.

y² - 48y +24² + 3 - 24² = 0

(y-24)² = 24² - 3 = 576-3 =573

y-24 = the square root of 24²-3 = plus or minus the square root of 573, which is slightly less than 24

The square root of 573 rounded to 3 decimal places is 23.937.

y= 24 + almost 24 and 24- almost 24

Rounded to 3 decimal places is y=47.937 x=0.063

or y=0.063 and x = 47.937

They sum to 48

Their reciprocals sum to 1/.063 + 1/47.937 = 15.87 + 0.021 which is close to 16, but a little off due to rounding approximations.

Multiply them for the product xy = (0.063)((47.937) = 3.020