Question

find two natural numbers,the sum of whose squares is 25 times tjeir sum and also equal to 50 times their difference. solve by one variable

Answer 1

Let x be the larger and y be the smaller. x² + y² = 25(x + y) = 50(x - y) 25(x + y) = 50(x - y) Divide both sides by 25 x + y = 2(x - y) x + y = 2x - 2y 3y = x Substitute 3y for x in: x² + y² = 25(x + y) (3y)² + y² = 25(3y + y) 9y² + y² = 75y + 25y 10y² = 100y y² = 10y y² - 10y = 0 y(y - 10) = 0 y = 0, y - 10 = 0 y = 10 0 is not a natural number, so y = 10 and since 3y = x 3(10) = x 30 = x So the two natural numbers are 30 and 10. Checking: The sum of their squares is 30²+10² = 900+100 = 1000 Their sum is 30+10 = 40 25 times 40 = 1000. That checks. Their difference is 30-10 = 20 50 times 20 = 1000. That checks and so the answers are indeed 30 and 10.
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Answer 2

Refers to attachment....!!!

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