SOLUTION: If x= 2+√3 and y=2-√3 the the value of 1/x^2 + 1/y^2 is ?

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Question 610778: If x= 2+√3 and y=2-√3 the the value of 1/x^2 + 1/y^2 is ?
Answer by solver91311(24713) About Me  (Show Source):
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Use the pattern



To expand the two denominators. Then collect like terms.

Then rationalize the resulting denominators by multiplying each of the fractions by 1 in the form of the conjugate of the denominator divided by itself. That is:

If the denominator is of the form , multiply the fraction by 1 in the form of . Recall that the product of two conjugates is the difference of two squares.

John

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