Question

Divide the number 24 into two parts such as that the ratio of their product to sum of their squares is 3:10.

Answer 1

answer is 20 and 4 and it is correct

Answer 2

AnStep-by-step explanation:

x + y = 24

x = 24 - y

xy : x²+y² = 3 : 10

xy/x²+y² = 3/10 )cross-multiplication)

10xy = 3x²+3y²

10y(24-y) = 3(24-y)(24-y) + 3y²

240y - 10y² = 1728 - 144y + 3y² + 3y²

240y + 144y = 1728 + 6y² + 10y²

1728 - 384y + 16y² = 0

16y² - 384y + 1728 = 0 (dividing the equation by 16)

y² - 24y + 108 = 0

y² - 6y - 18y + 108

y(y-6) - 18(y-6)

(y-18)(y-6)

The two parts of 24 are 18 and 6