3x + y = 1 => y = 1 - 3x
=> M = 3x2 + (1 - 3x)2 = 3x2 + 1 - 6x + 9x2 = 12x2 - 6x + 1
= 12.(x2 - \(\frac{1}{2}\).x + \(\frac{1}{12}\)) = 12. [(x2 - 2.x.\(\frac{1}{4}\) + \(\frac{1}{16}\)) - \(\frac{1}{16}\)+ \(\frac{1}{12}\)]
= 12. (x - \(\frac{1}{4}\))2 - \(\frac{12}{16}\) + 1 = 12. (x - \(\frac{1}{4}\))2 + \(\frac{1}{4}\) \(\ge\) 12. 0 + \(\frac{1}{4}\) = \(\frac{1}{4}\) với mọi x
Vậy Min M = \(\frac{1}{4}\) khi x = \(\frac{1}{4}\)
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