Question

Find two natural numbers the sum of whose squares is 25 times

Answer 1

Answer:et the numbers be x and y

according to question,

x² + y² = 25(x+y)  ____________(1)

x² + y² = 50(x-y)   ____________(2)

from (1) and (2)

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

⇒ x+y = 2(x-y) = 2x - 2y

⇒ y+2y = 2x-x

⇒ 3y = x

⇒ x = 3y

putting x in (1)

x² + y² = 25(x+y)

⇒ (3y)² + y² = 25(3y+y)

⇒9y²+y²=25×4y

⇒10y²=100y

⇒y² = 10y

⇒ y = 0 or 10

but y≠0 as y is a natural number

So y = 10

 x = 3y = 30

two numbers are 10 and 30

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