1.

The value of \(\frac{1}{{(7\; + \;4\sqrt 3 })^2} + \frac{1}{{(7\; - \;4\sqrt 3 )^2}}\) is1. 1942. 1543. 1844. 149

Answer» Correct Answer - Option 1 : 194

Given:

\(\frac{1}{{(7\; + \;4√ 3 })^2} + \frac{1}{{(7\; - \;4√ 3 )^2}}\)

Concept used:

Componendo and dividendo

Calculation:

\(\frac{1}{{(7\; + \;4√ 3 })^2} + \frac{1}{{(7\; - \;4√ 3 )^2}}\)

⇒ \(\frac{(7\; - \;4√3)^2}{{(7\; + \;4√ 3 })^2(7\; - \;4√3)^2} + \frac{(7\; + \;4√3)^2}{{(7\; - \;4√ 3 )^2(7 \;+\;4√3)^2}}\)

⇒ \(\frac{(7\; - \;4√3)^2}{{1}} + \frac{(7\; + \;4√3)^2}{1}\)

⇒ 72 + (4√3)2 – 2 × 7 × 4√3 + 72 + (4√3)2​ + 2 × 7 × 4√3

⇒ 49 + 48 – 56√3 + 49 + 48 + 56√3

⇒ 49 + 48 + 49 + 48

⇒ 194

∴ Required value is 194


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