Question

x1 si x2 sint solutiile ecuatiei x²-13x+14=0 aflati valoarea expresiei :
a)x1²+x2²
b)(x1-x2)²

Answer 1

x^2-13x+14=0
a=1 b=-13 c=14
∆=b^2-4ac=(-13)^2-4•1•14=169-56=113=>√∆=√113
-b-√∆ +13-√113.
X1=______=________
2a. 2
=>S(+13-√113/2,+13+√113/2)
-b+√∆ +13+√113
X2=_______=________
2a. 2

a) 169-113/4 + 169+113/2 =56/4 + 282/4= 14 + 282/4= 56+282/4= 338/4= 169/2
b) (13-√113/2 - 13+√113/2)^2= (13-13-√113-√113/2)=26-0/2=26/2=13