Write the quadratic equation and solve by using the general formula. "Find two consecutive numbers in which the double of the square of the smaller number plus the square of the greater number is 121"

6 and 7

Step-by-step explanation:

Let the numbers be x and x + 1

We can form and equation as:

2(x²) + (x+1)² = 121

2x² + (x + 1)(x + 1) = 121

2x² + x² + x + x + 1 = 121

3x² + 2x = 121 - 1

3x² + 2x = 120

3x² + 2x - 120 = 0

3x² - 18x + 20x - 120 = 0

3x(x - 6) + 20(x - 6)

Therefore, x - 6 = 0

x = 0 + 6

x = 6

The numbers are 6 and 7