Solve application problems using quadratic equations.

Question

A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49. Find the numbers.

Answer 1

y is the larger and y-2 is the smaller.

4y + (y-2)² = 49

4y + y² - 4y + 4 = 49

y² = 45

y - 3√5 and x = 3√5√ -2