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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 1 · Set 2 · Q22
If y=(x+√(x^2-1))^2, then show that (x^2-1)((d y)/(d x))^2=4 y^2.
If $\displaystyle y=\left(x+\sqrt{x^{2}-1}\right)^{2}$, then show that $\displaystyle \left(x^{2}-1\right)\left(\frac{d y}{d x}\right)^{2}=4 y^{2}$.
Marking-scheme solution
$\displaystyle \frac{d y}{d x}=2\left(x+\sqrt{x^{2}-1}\right)\left(1+\frac{x}{\sqrt{x^{2}-1}}\right)=\frac{2\left(x+\sqrt{x^{2}-1}\right)^{2}}{\sqrt{x^{2}-1}}$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.