Réponse:
1)
f(x) = x² + ¼(10-x)²
= x² + ¼(10²-2×10×x+x²)
= x² + ¼(100-20x+x²)
= x² + 25 - 5x + 0,25x²
= 1,25x² - 5x + 25
2)
1,25(x-2)²+20 =
1,25(x²-4x+4)+20 =
1,25x² - 5x + 5 + 20 =
1,25x² - 5x + 25 =
f(x)
3)
f(x)=25
1,25x²-5x+25=25
1,25x²-5x=0
x(1,25x-5)=0
x=0 ou 1,25x-5=0
x= 0 ou x = 4