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Question

If $$\sqrt{x+y}+\sqrt{y-x}=c$$, then $$\dfrac{d^2y}{dx^2}$$ is


A
2c
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B
2c2
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C
2c2
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D
2c
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Solution

The correct option is C $$\displaystyle \frac{2}{c^2}$$
$$\sqrt{x+y}=c-\sqrt{y-x}$$
On squaring we get,
$$2x-c^2=-2c\sqrt{y-x}$$
Again squaring we get,
$$y = \dfrac{(2x-c^2)^2}{4c^2}+x$$
$$y'=\dfrac{4(2x-c^2)}{4c^2}+1$$
$$y''=\dfrac{8}{4c^2}=\dfrac{2}{c^2}$$
Option C

Mathematics

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