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The sum of the squares of two numbers is 41. The difference of the squares of these numbers is 9 What are the numbers? |
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Answer» Explanation:Given :SUM of the square of two numbers is 41.The difference of the squares of these numbers is 9.To Find :Numbers.Solution :Let, first number be "R" and second number be "S" respectively. Case (I) : Sum of the square of two numbers is 41.=> R² + S² = 41______(1)Case (II) : The difference of the squares of these numbers is 9.=> R² - S² = 9_______(2)From equation (1) & (2),R² + S² = 41R² - S² = 9+ + +_________2R² = 50=> R² = 50/2=> R² = 25=> R = √25=> R = 5 Put R = 5 in eqn. (1),=> 5² + S² = 41=> 25 + S² = 41=> S² = 41 - 25=> S² = 16=> S = √16=> S = 4SO,First number = R = 5Second number = S = 4Hence :The first number and second number is 5 and 4 respectively. |
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