Stumped on this one

Question

The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number. What are the numbers?

Answer 1

The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number. What are the numbers?

Detailed Solution:

x² + y² = 1156

y = (3x²)^1/2

= (√3)x

x² + ((√3)x)² = 1156

x² + 3x² = 1156

4x² = 1156

x² = 289

x = 17

y = (√3)(17)

y = 17√3

The two numbers: (x, y) = (17, 17√3)

Check: x² + y² = 1156 ==> (17)² + (17√3)² = 1156 ==> 1156 = 1156

Answer 2

x² + y² = 1156

y = √3x²

Solve by substitution.