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The difference of square of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers. |
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Answer» Let the smaller natural number be x and larger natural number be yHence x2= 4y → (1)Given y2– x2= 45⇒ y2– 4y = 45⇒y2– 4y – 45 = 0⇒y2– 9y + 5y – 45 = 0⇒y(y – 9) + 5(y – 9) = 0⇒(y – 9)(y + 5) = 0⇒ (y – 9)= 0 or (y + 5) = 0∴ y = 9 or y = -5But y is natural number, hence y ≠ - 5Therefore, y = 9Equation (1) becomes,x2= 4(9) = 36∴ x = 6Thus the two natural numbers are 6 and 9. |
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