Question

21. Find two natural numbers, the sum of whose squares is 25 times their
sum and also equal to 50 times their difference.
please solve it by quadratic equation​

Answer 1

Answer:

let two numbers be x,y

according to question,

x²+y²=25(x+y)

x²+y²=50(x-y)

25(x+y)=50(x-y)

x+y=2(x-y)

x+y=2x-2y

x=3y

=>9y²+y²=25(3y+y)

10y²=25(4y)

2y²=5(4y)

y²=10y

y²-10y=0

y(y-10)=0

y=0,y=10

=>x=0,x=30

therefore,x=30,y=10