The product of two numbers is 10 more than 5 times the sum times the sum. Find the numbers if the numbers are in a ratio 5 : 6.

The product of two numbers is 10 more than 5 times the sum times the sum. Find the numbers if the numbers are in a ratio 5 : 6. Correct Answer 10, 12

Let the ratios be in terms of x. The numbers will be 5x and 6x. The product of the numbers = 30x2 The sum of the numbers = 6x + 5x = 11x Now it is giving that 30x2 = 5 * 11x + 10 = 55x + 10 30x2 = 55x + 10 On solving the quadratic equation, we get x = 2 The numbers are 10 and 12.
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