The least positive integer that should be sub | vedclass

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Question

(C) Let the given expression be $E = 3011 	imes 3012$.We can write $3012$ as $(3011 + 1)$.So,$E = 3011 	imes (3011 + 1) = (3011)^2 + 3011$.To make t

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$3011$

Vedclass · Answer

(C) Let the given expression be $E = 3011 	imes 3012$.We can write $3012$ as $(3011 + 1)$.So,$E = 3011 	imes (3011 + 1) = (3011)^2 + 3011$.To make this expression a perfect square,we need to subtract a value $x$ such that $(3011)^2 + 3011 - x = k^2$ for some integer $k$.If we subtract $3011$,we get $(3011)^2 + 3011 - 3011 = (3011)^2$,which is a perfect square.Thus,the least positive integer to be subtracted is $3011$.

The least positive integer that should be subtracted from $3011 \times 3012$ so that the difference is a perfect square,is

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