SOLUTION: The product of two numbers is 2, and the sum of their squares is 17/2. Find the numbers.

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Question 194321This question is from textbook Algebra and Trigonometry: Structure and Method (2nd)
: The product of two numbers is 2, and the sum of their squares is 17/2. Find the numbers. This question is from textbook Algebra and Trigonometry: Structure and Method (2nd)

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x & y be the numbers.
1) xy=2
2) x^2+y^2=17/2
.
1) y=2/x
2)
x^2+(2/x)^2=17/2 substitute 2/x for y
x^2+4/x^2=17/2
2x^4+8=17x^2 multiply each side by 2x^2 (LCM) to eliminate fractions.
2x^4-17x^2+8=0
2x^4-x^2-16x^2+8=0
x^2(2x^2-1)-8(2x^2-1)=0
(x^2-8)(2x^2-1)=0
.
x^2=8
x=+-sqrt(8)
=+-sqrt(4*2)
=+- 2sqrt(2)
.
2x^2=1
x^2=1/2
x=+-sqrt(1/2)
=+- 1/sqrt(2)
=+- sqrt(2)/2
.
x=-2sqrt(2), y=-sqrt(2)/2
x=2sqrt(2), y=sqrt(2)/2
and vice versa (4 answers)
.
Ed