Question

The sum of the squares of two nonnegative numbers is 327. The product of the two numbers is 101. What is the sum of the two numbers?

Answer 1

A) x² + y² = 327
B) x * y = 101
Solving equation B for y²
B) y² = 10,201 / x²
Substituting this into equation A)
x² + 10,201 / x² = 327
x^4 + 10,201 = 327x²
x^4  -327x²  + 10,201 = 0
Using the quartic equation calculator: http://www.1728.org/quartic.htm
x1 = 17.090169943749476
x2 = 5.909830056250525
 
x1 * x2 = 101
x1 + x2 = 23