\(\rm\left(\frac{25}{9}\right)^{x+1}\left(\frac{81}{625}\right)^{x-1}=\frac{9}{25} \)ആണെങ്കിൽ, x ന്റെ മൂല്യം കണ്ടെത്തുക.

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RRB Group D 16 Sept 2022 Shift 3 Official Paper

Answer 1

കണക്കുകൂട്ടൽ:

\(\rm\left(\frac{25}{9}\right)^{x+1}\left(\frac{81}{625}\right)^{x-1}=\frac{9}{25} \ \)

⇒\((\frac{25}{9})^{(x + 1)}(\frac{9²}{25²})^{(x-1)}\)= \(\frac{ 9}{25}\)

⇒\((\frac{25^{(x+1)}}{9^{(x+1)}})(\frac{9^{2(x-1)}}{25^{2(x-1)}})\) = \(\frac{ 9}{25}\)

⇒ \(\frac{9^{2(x-1)-(x+1)}}{25^{2(x-1)-(x+1)}}\) = \(\frac{ 9^1}{25^1}\)

⇒ 2(x - 1) - (x + 1) = 1

⇒ 2x - 2 - x - 1= 1

⇒ x = 4

അതിനാൽ, x ന്റെ ആവശ്യമായ മൂല്യമാണ് 4.

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