Question

scrieti ecuatia de gradul 2 cu necunoscuta x, care are solutiile 4-√3 si 4+√3

Answer 1

x₁=4-√3
x₂=4+√3
s=x₁+x₂=4-√3+4+√3=8
p=x₁*x₂=(4-√3)(4+√3)=16-3=13
x²-sx+p=0
x²-8x+13=0

Answer 2

$Daca \ S=\{4-\sqrt3; \ 4+\sqrt3\}, \ atunci : \\ \Delta\ \textgreater \ 0, \ iar \ \sqrt3=\sqrt{\Delta} \ \ \ \Rightarrow \Delta=3 \\ \Delta=b^2-4ac=3 \\ ax^2-bx+c=0 \\ x_1= \frac{4-\sqrt3}{1} = \frac{-b-\sqrt\Delta}{2a} ;\ \ \\2a=1 \ \Rightarrow a=\frac{1}{2}=0,5;\\ \ -(-b)=b=4; \\ 0,5x^2-4x+c=0 \\ \Delta=4^2-4 \cdot 0,5 \cdot c=3 \\ 16-2c=3 \\ 2c=16-3=13 \\ c=\frac{13}{2}=6,5 \\ \Rightarrow \boxed{0,5x^2-4x+6,5=0}$