Question
Download Solution PDFWhat is the value of \(\frac{{1 + a}}{{{a^{1/2}} + {a^{ - 1/2}}}} - \frac{{{a^{1/2}} + {a^{ - 1/2}}}}{{1 + a}} + {a^{ - 1/2}}?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
{[(1 + a) / (a1/2 + a-1/2) + a-1/2] – [(a1/2 + a-1/2) / (1 + a)]}
⇒ {[(1 + a) + (a1/2 + a-1/2)(a-1/2) / (a1/2 + a-1/2)] – [(a1/2 + a-1/2) / (1 + a)]}
⇒ {[(2 + a + a-1) / (a1/2 + a-1/2)] – [(a1/2 + a-1/2) / (1 + a)]}
⇒ {[(2 + a + a-1)(1 + a) – (a1/2 + a-1/2)2] / [(a1/2 + a-1/2)(1 + a)]}
⇒ {[(a2 + 3a + a-1 + 3) – (a + a-1 + 2)] / [(a1/2 + a3/2 + a-1/2 + a1/2)]}
⇒ {(a2 + 2a + 1) / (2a1/2 + a3/2 + a-1/2)}
Taking a1/2 common from the numerator
⇒ a1/2[(2a1/2 + a3/2 + a-1/2)] / [( 2a1/2 + a3/2 + a-1/2)]
⇒ a1/2 (1) = √a
∴ the correct option is 1Last updated on Jul 12, 2025
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