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The number of solution pairs (x , y) of the simultaneous equations `log_(1//3) (x + y) + "log"_(3) (x-y) = 2` and `2^(y^(2)) = 512^(x + 1)` is |
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Answer» Correct Answer - B `"log"_(3^(-1)) (x + y) + "log"_(3)( x - y) = 2` `-"log"_(3) (x +y) + "log"_(3) (x - y) = 2` `"log"_(3) ((x - y)/(x + y)) = 2 ` `( x - y)/(x + y) = 9` `2^(y^(2)) = (2^(9))^(x + 1)` `2^(y^(2)) = 2^(9^(x + 1))` `y^(2) = 9(x + 1)` Solve eliminate y `16x^(2) - 225 x -225 = 0 ` x = 15 , `(-15)/(16)` At x = 15 , y = `-12` x = `(-15)/(16) , y = (3)/(4)` ( not possible ) only sol . x = 15, y = `-12` only one sol. |
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