x1 + x2 = 2
x1² + x2² = 16
x1² + x2² = 16
(x1 + x2)² - 2x1x2 = 16
2² - 2x1x2 = 16
-2x1x2 = 16 - 4
-2x1x2 = 12
x1 * x2 = - 6
x1 + x2 = 2
x1 * x2 = -6
-b/a = 2
c/a = -6
-b = 2a
c = -6a
b = -2a
c = -6a
ax² + bx + c = 0
dla np a = 1 otrzymujemy
b = -2 * 1 = -2
c = -6 * 1 = -6
czyli otrzymujemy równanie:
x² - 2x - 6 = 0 ------- odpowiedź
spr.
x² - 2x - 6 = 0
Δ = (-2)² - 4 * 1 * (-6) = 4 + 24 = 28
√Δ = √28 = 2√7
x1 = (2 - 2√7)/2 = 1 - √7
x2 = (2 + 2√7)/2 = 1 + √7
x1 + x2 = 1 - √7 + 1 + √7 = 2 tyle miała wyjść suma pierwiastków x1 i x2
x1² + x2² = (1 - √7)² + (1 + √7)² = 1 - 2√7 + 7 + 1 + 2√7 + 7 = 16 czyli też dobrze wyszło