- #1
Rach123
- 6
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Homework Statement
x^2+y^2=5, 1/x^2+1/y^2=5/4The Attempt at a Solution
I have rearranged the 1st equation: x^2=5-y^2
Then substitued this into the 2nd equation: 1/(5-y^2)+1/y^2=5/4
Found a common denominator: 5/(5x^2-x^4)=5/4
Multiply by the denominator: 5=(25x^2-5x^4)/4
Multiply by 4: 20=25x^2-5x^4
Now I have two methods for factorising which results in different answers: method 1: 4=5x^2-x^4
multiply by -1: x^4-5x^2=-4
x^2(x^2-5)=-4 which gives +or- 1 as the only solutions as -4^0.5 has no real solutions
However, method 2: 4=5x^2-x^4
4=x^2(5-x^2) which gives +or-2 AND +or-1 as the solutions.
Could anybody tell me where I have gone wrong and why the second method gives 4 solutions.