If $x^{2} + y^{2} = 2$ and $y^{11} + A . y^{- 3} = 0$ then $A$ is

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Solution

$x^{2} + y^{2} = 2$

$y^{11} + A . y^{- 3} = 0$

$y^{11} + \frac{A}{y^{3}} = 0 \to [y^{14} + A] = 0$

$y^{2} = 2 - x^{2}$

$(y^{2})^{7} + A = 0$

$(2 - x^{2})^{7} + A = 0$

${A = - [2 - x^{2}]^{7}}$

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