Question

If x=9+4√5 and xy=1,then find the value of ¹/x²+¹/y²

Answer 1

Answer:

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Step-by-step explanation:

X = 9 + 4√5

xy = 1

y = 1/x

y = 1/(9 + 4√5)

By rationalization,

y = 9 - 4√5

××××××××××××××

x², y²

=> (9 + 4√5)², (9 - 4√5)²

=> 81 + 80+ 72√5 =x²

=> 161 + 72√5 = x² = 1 / y²

=> 81 + 80 - 72√5 = y²

=> 161 - 72√5= y² = 1 / x²

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