SOLUTION: 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.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 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.      Log On


   

Question 1118596: 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 by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28y-x=2%2C4y%2Bx%5E2=49%29

y=x%2B2
-
4%28x%2B2%29%2Bx%5E2=49
4x%2B8%2Bx%5E2=49
x%5E2%2B4x%2B8-49=0
x%5E2%2B4x-41=0

x=%28-4%2Bsqrt%2816%2B4%2A41%29%29%2F2

x=%28-4%2Bsqrt%28180%29%29%2F2

180=10*18=2*5*3*6=2*5*3*2*3=2*2*3*3*5

x=%28-4%2B6%2Asqrt%285%29%29%2F2

x=-2%2B3%2Asqrt%285%29-----------the smaller number

y=3%2Asqrt%285%29-------------the larger number