Question:১১.`x = (4ab)/(a + b)` হলে, দেখাও যে, `(x + 2a)/(x - 2a) + (x + 2b)/(x + 2b) = 2, a != b`
Answer ১০. সমাধান: দেওয়া আছে, `x = (4ab)/(a + b)` বা, `x = (2a xx 2b)/(a + b)` `:. x/(2a) = (2b)/(a + b)` এবং `x/( 2b) = (2a)/(a + b)` যখন, `x/(2a) = (2b)/(a + b)` তখন, `(x + 2a)/(x - 2a) = (2b + a + b)/(2b - a - b)` [ যোজন-বিয়োজন করে ] `:. (x + 2a)/(x - 2a) = (a + 3b)/(b - a)` .........(i) আবার, যখন `x/( 2b) = (2a)/(a + b)` তখন, `(x + 2b)/(x - 2b) = (2a + a + b)/(2a - a - b)` [ যোজন-বিয়োজন করে ] `:. (x + 2b)/(x - 2b) = (3a + b)/(a - b)`..........(ii) (i) নং এবং (ii) নং সমীকরণ যোগ করে পাই, `(x + 2a)/(x - 2a) + (x + 2b)/(x - 2b) = (a + 3b)/(b - a) + (3a + b)/(a - b)` `= (a + 3b)/(b - a) + (3a + b)/( - (b - a))` `= (a + 3b)/(b - a) - (3a + b)/(b - a)` `= (a + 3b - (3a + b))/(b - a)` `= (2b - 2a)/(b - a)` `= (2(b - a))/((b - a))` `= 2` `:. (x + 2a)/(x - 2a) + (x + 2b)/(x + 2b) = 2` ( দেখানো হলো )
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১১.`x = (4ab)/(a + b)` hole, dekhao je, `(x + 2a)/(x - 2a) + (x + 2b)/(x + 2b) = 2, a != b`