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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
Question
Show that, $\log \left|\sqrt{x^2+1}+x\right|+\log \left|\sqrt{x^2+1}-x\right|=0$.
✓

Answer

$ \text { L.H.S. }=\log \left|\sqrt{x^2+1}+x\right|+\log \left|\sqrt{x^2+1}-\mathrm{x}\right|$
$=\log \left|\left(\sqrt{x^2+1}+x\right)\left(\sqrt{x^2+1}-x\right)\right|$
$=\log \left|x^2+1-x^2\right|$
$=\log 1$
$=0$
$=\text { R.H.S. }$

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