Question:৯.`a/b = c/d` হলে, দেখাও যে, (i). `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)` (ii) `(ac + bd)/(ac - bd) = (c^2 + d^2)/(c^2 - d^2)`
Answer সমাধান: ৯. (i).দেওয়া আছে,`a/b = c/d` ধরি,`a/b = c/d = k` `:. a = bk` এবং `c = dk` বামপক্ষ `=(a^2 + ab + b^2)/(a^2 - ab + b^2)` `=((bk)^2 + bk xx b + b^2)/((bk)^2 - bk xx b + b^2)` `=(b^2k^2 + b^2k + b^2)/(b^2k^2 - b^2k + b^2)` `=(b^2(k^2 + k +1))/(b^2(k^2 - k + 1))` `=(k^2 + k + 1)/(k^2 - k + 1)` ডানপক্ষ `=(c^2 + cd + d^2)/(c^2 - cd + d^2)` `=((dk)^2 + dk xx d + d^2)/((dk)^2 - dk xx d + d^2)` `=(d^2k^2 + d^2k + d^2)/(d^2k^2 - d^2k + d^2)` `=(d^2(k^2 + k + 1))/(d^2(k^2 - k + 1))` `=(k^2 + k + 1)/(k^2 - k + 1)` `:. (a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)`( দেখানো হলো ) (ii).দেওয়া আছে,`a/b = c/d` ধরি,`a/b = c/d = k` `:. c = dk` `a = bk` বামপক্ষ `=(ac + bd)/(ac - bd)` `=(bk xx dk + bd)/(bk xx dk - bd)` `=(bdk^2 + bd)/(bdk^2 - bd)` `=(bd(k^2 + 1))/(bd(k^2 - 1))` `=(k^2 + 1)/(k^2 - 1)` ডানপক্ষ `=(c^2 + d^2)/(c^2 - d^2)` `=((dk)^2 + d^2)/((dk)^2 - d^2)` `=(d^2k^2 + d^2)/(d^2k^2 - d^2)` `=(d^2(k^2 + 1))/(d^2(k^2 - 1))` `=(k^2 + 1)/(k^2 - 1)` `:. (ac + bd)/(ac - bd) = (c^2 + d^2)/(c^2 - d^2)` ( দেখানো হলো )
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৯.`a/b = c/d` hole, dekhao je, (i). `(a^2 + ab + b^2)/(a^2 - ab + b^2) = (c^2 + cd + d^2)/(c^2 - cd + d^2)` (ii) `(ac + bd)/(ac - bd) = (c^2 + d^2)/(c^2 - d^2)`