Question

x² + y²+ 1/x²+ 1/y² =4. Find x²+y²​

Answer 1

Answer:

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Answer 2

Answer:

2

Step-by-step explanation:

As

$({x}^{2} + { (\frac{1}{x}) }^{2} ) + ({y}^{2} + { (\frac{1}{y}) }^{2} ) = 4$

Using AM-GM inequality, we get

x = ±1 and y = ±1

So x² = y² = 1

Hence x²+y²= 1 + 1 = 2

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