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The value of t for which \({m^2} - \frac{5}{2}m + t\) will be a perfect square, is

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The value of t for which \({m^2} - \frac{5}{2}m + t\) will be a perfect square, is


1). \(\frac{{25}}{4}\)
2). \(\frac{{25}}{{16}}\)
3). \(\frac{5}{2}\)
4). \(\frac{5}{4}\)


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3 vote
Answered by on | Votes 3 |

(a – b)2 = a2 + b2 – 2ab

$(\begin{array}{l} {m^2} - \frac{5}{2}m + t\\ = {m^2} - \frac{5}{2}m + \frac{{25}}{{16}} - \frac{{25}}{{16}} + t\\ = {\left( {m - \frac{5}{4}} \right)^2} + t - \frac{{25}}{{16}} \end{array})$ 

Thus, value of t for which it is a perfect square is 25/16

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