Question

Find two positive integers such that the sum of the first number and four times the
second number is 1000, and the product of the numbers is as large as possible.​

Answer 1

Answer:

tgkh....................................

Answer 2

The two positives numbers will be 125 and 500.

• Given,

(x+4y) = 1000            ……….(i)

• Using Arithmetic mean and geometic mean relation,

[(x+4y) / 2]  ≥ √(x*4y)

Using value from (i),

250 ≥ √(x*y)

Squaring both sides,

xy = 62500

y = 62500 / x   ……….(ii)

• Putting the value of y from (i) into (ii) and making equation,

x + (250000/x) = 1000

x2 – 1000x + 250000 = 0

x = 500    ………(iii)

• Putting value of x from (iii) into (ii),

y = 125