\(\frac{{1 + a}}{{{a^{1/2}} + {a^{ - 1/2}}}} - \frac{{{a^{1/2}} + {a^{ - 1/2}}}}{{1 + a}} + {a^{ - 1/2}}\) का मान कितना है?

Question

Question

This question was previously asked in

SSC CGL Previous Paper 14 (Held On: 11 August 2017 Shift 2)

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Answer 1

दिया गया है: {[(1 + a)/(a^1/2 + a^-1/2) + a^-1/2] – [(a^1/2 + a^-1/2) / (1 + a)]}

⇒ {[(1 + a) + (a^1/2 + a^-1/2)(a^-1/2) / (a^1/2 + a^-1/2)] – [(a^1/2 + a^-1/2)/(1 + a)]}

⇒ {[(2 + a + a^-1) / (a^1/2 + a^-1/2)] – [(a^1/2 + a^-1/2) / (1 + a)]}

⇒ {[(2 + a + a^-1)(1 + a) – (a^1/2 + a^-1/2)²] / [(a^1/2 + a^-1/2)(1 + a)]}

⇒ {[(a² + 3a + a^-1 + 3) – (a + a^-1 + 2)] / [(a^1/2 + a^3/2 + a^-1/2 + a^1/2)]}

⇒ {[(a² + 2a + 1)] / [(2a^1/2 + a^3/2 + a^-1/2)]}

अंश में से a^1/2 सार्व लेने पर,

⇒ a^1/2[(2a^1/2 + a^3/2 + a^-1/2)] / [( 2a^1/2 + a^3/2 + a^-1/2)]

⇒ a^1/2(1) = √a

∴ 1) सही उत्तर है।