If x- a - 1 - a -y- a - 1 - a - then the value of x 4 - y 4 -2 x 2 y 2 is-

The correct option is A 16 Given, x = √(a)+1√(a) ; y = √(a) 1√(a) so, x^2 = a+1a+2 ; y^2 = a+1a 2 Ans, x^2 y^2 = a+1a+2 a 1a+2 = 4 Now, ...

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Finding Square Root of a Number

If x=√ a + ...

Question

If $x = \sqrt{a} + \frac{1}{\sqrt{a}}, y = \sqrt{a} - \frac{1}{\sqrt{a}}$ , then the value of
$x^{4} + y^{4} - 2 x^{2} y^{2}$ is:

16

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20

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10

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5

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\sqrt{1 - x^{4}} + \sqrt{1 - y^{4}} = k (x^{2} - y^{2}),

\frac{d y}{d x} = \frac{x \sqrt{1 - y^{4}}}{y \sqrt{1 - x^{4}}}

x = a^{1 / 2} + a^{- 1 / 2}, y = a^{1 / 2} - a^{- 1 / 2}

(x^{4} - x^{2} y^{2} - 1) + (y^{4} - x^{2} y^{2} + 1)

x^{4} + 2 x^{2} y^{2} + y^{4}

x^{2} + y^{2} = t + \frac{1}{t}

x^{4} + y^{4} = t^{2} + \frac{1}{t^{2}}

\frac{d y}{d x} = - \frac{y}{x}

y = \frac{1}{x},

\frac{d y}{\sqrt{1 + y^{4}}} + \frac{d x}{\sqrt{1 + x^{4}}} + 1

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