यदि abc = 5, (\({1 \over 1 \ + \ a \ + \ b^{-1} }\) + \({1 \over 1 \ + \ b \ + \ 5 c^{-1}}\) +\(\frac{1}{1+\frac{c}{5}+a^{-1}}\) \(\)) का मान क्या है?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 3)

Answer 1

दिया गया है:

यदि abc = 5

प्रयुक्त अवधारणा:

abc = 5

⇒ ac = \(5\over b \)

⇒ (b)-1

⇒ b = \(5\over ac\)

गणना:

\({1 \over 1 \ + \ a \ + \ b^{-1} }\) + \({1 \over 1 \ + \ b \ + \ 5 c^{-1}}\) + \(\frac{1}{1+\frac{c}{5}+a^{-1}}\)

⇒\(\frac{1}{1+\frac{ac}{5}+a}\) + \(\frac{1}{1+\frac{5}{ac}+5c^{-1}}\) + \(\frac{1}{1+\frac{1}{ab}+a^{-1}}\)

⇒\(5\over5+5a+ac \)\(+\) \(ac\over5+5a+ac \) \(+\) \(a\over5+a+ac \)

⇒\(a+5+ac\over5+a+ac \)

⇒\(1\)

अतः, ( \({1 \over 1 \ + \ a \ + \ b^{-1} }\)+\({1 \over 1 \ + \ b \ + \ 5 c^{-1}}\)+\(\frac{1}{1+\frac{c}{5}+a^{-1}}\)), का मान 1 है।

Shortcut Trick माना a = b = 1 और c = 5

अब, प्रश्न के अनुसार,

⇒ \({1 \over 1 \ + \ 1 \ + {5 \over 5 }}\) \(\frac{1}{1+\frac{5}{5}+ {1}}\) + \(\frac{1} {1+\frac{5}{5}+ {1}}\)

⇒ 1/3 + 1/3 + 1/3

⇒ 3/3 = 1