MCQ
If $x + \sqrt {({x^2} + 1)} = a,$ then $x =$
- A${1 \over 2}(a + 1/a)$
- ✓${1 \over 2}(a - 1/a)$
- C$(a + {a^{ - 1}})$
- DNone of these
✓
Answer
Correct option: B.
${1 \over 2}(a - 1/a)$
b
(b) $x + \sqrt {{x^2} + 1} = a \Rightarrow \sqrt {{x^2} + 1} = a - x$
(b) $x + \sqrt {{x^2} + 1} = a \Rightarrow \sqrt {{x^2} + 1} = a - x$
$ \Rightarrow $${x^2} + 1 = {(a - x)^2} = {x^2} - 2ax + {a^2}$
$ \Rightarrow $$x = {{1 - {a^2}} \over { - 2a}} = {{{a^2} - 1} \over {2a}} = {1 \over 2}\left( {a - {1 \over a}} \right)$.
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