Question:১২. প্রমাণ কর: `(2^(p + 1) .3^(2p - q) .5^(p + q) .6^q)/(6^p .10^(q + 2) .15^p) = 1/50`
Answer সমাধান: বামপক্ষ `= (2^(p + 1) .3^(2p - q) .5^(p + q) .6^q)/(6^p .10^(q + 2) .15^p)` `= (2^(p + 1) .3^(2p - q) .5^(p + q) .(2 xx 3)^q)/((2 xx 3)^p .(5 xx 2)^(q + 2) .(3 xx 5)^q)` `= (2^(p + 1) .3^(2p - q) .5^(p + q) .2^q .3^q)/(2^p .3^p .5^(q + 2) .2^(q + 2) .3^p .5^p)` `= (2^(p + q + 1) .3^(2p - q - q) .5^(p + q))/(2^(p + q + 2) .3^(p + p) .5^(q + p + 2))` `= (2^(p + q + 1) .3^(2p) .5^(p + q))/(2^(p + q + 2) .3^(2p) .5^(p + q + 2))` `= 2^((p + q + 1) - (p + q + 2)) .3^(2p - 2p) .5^((p + q) - (p + q + 2))` `= 2^(p + q + 1 - p - q - 2) .3^0 .5^(p + q - p - q - 2)` `= 2^(- 1) . 1 . 5^(- 2)` `= 1/2 . 1 . 1/5^2` `= 1/2 . 1 . 1/25` `= 1/50` `:. (2^(p + 1) .3^(2p - q) .5^(p + q) .6^q)/(6^p .10^(q + 2) .15^p) ` `= 1/50` প্রমাণিত
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১২. proman karo: `(2^(p + 1) .3^(2p - q) .5^(p + q) .6^q)/(6^p .10^(q + 2) .15^p) = 1/50`