a) x² - x + 1
= x² - 2.x.1/2 + 1/4 + 3/4
= (x² - 2.x.1/2 + 1/4) + 3/4
= (x - 1/2)² + 3/4
b) x² + 3x + 4
= x² + 2.x.3/2 + 9/4 + 7/4
= (x² + 2.x.3/2 + 9/4) + 7/4
= (x + 3/2)² + 7/4
c) x⁴ - 4x² + 6
= x⁴ - 2.x².2 + 4 + 2
= (x² - 2)² + 2
d) 2x² + 6x - 15
= 2(x² + 3x - 15/2)
= 2(x² + 2.x.3/2 + 9/4 - 39/4)
= 2(x + 3/2)² - 39/2
e) x² - 5x + 9
= x² - 2.x.5/2 + 25/4 + 11/4
= (x² - 2.x.5/2 + 25/4) + 11/4
= (x - 5/2)² + 11/4
g) 3x² - 12x + 20
= 3.(x² - 4x + 20/3)
= 3.(x² - 2.x.2 + 4 + 8/3)
= 3.(x - 2)² + 8
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