SOLUTION: PreAP/GT Algebra II, teacher supplements the textbook with worksheets from College Algebra books. Worksheet titled SAT/ACT Test Prep #4. 3 parts to this problem: x^ + y^ = 16

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: PreAP/GT Algebra II, teacher supplements the textbook with worksheets from College Algebra books. Worksheet titled SAT/ACT Test Prep #4. 3 parts to this problem: x^ + y^ = 16      Log On


   



Question 104027: PreAP/GT Algebra II, teacher supplements the textbook with worksheets from College Algebra books. Worksheet titled SAT/ACT Test Prep #4.
3 parts to this problem:
x^ + y^ = 16
xy = 8
(x + y)^ = ?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + y^2 = 16
y^2 = 16 - x^2
y = sqrt%2816-x%5E2%29
:
xy = 8
substitute sqrt%2816-x%5E2%29for y, find x:
x*sqrt%2816-x%5E2%29 = 8
Square both sides
x^2(16-x^2) = 64
:
-x^4 + 16x^2 - 64 = 0; a quadratic equation
+x^4 - 16x^2 + 64 = 0; multiplied by -1
Factor:
(x^2 - 8)(x^2 - 8) = 0
x^2 = +8
x = sqrt%288%29
x = 2sqrt%282%29
:
Find y:
2sqrt%282%29*y = 8
y = 8%2F%282sqrt%282%29%29
y = 4%2Fsqrt%282%29


(x + y)^2 = ?
FOIL
(2sqrt%282%29+4%2Fsqrt%282%29)*(2sqrt%282%29+4%2Fsqrt%282%29) = ?
4(2) + 8sqrt%282%29%2Fsqrt%282%29 + 8sqrt%282%29%2Fsqrt%282%29 + 16%2F2 =
8 + 8 + 8 + 8 = 32