[tex]2x^{2} -13x+5=0[/tex]
По теореме Виета для этого уравнения:
x1 + x2 = -B = 13/2
x1 * x2 = C = 5/2
По теореме Виета для нового уравнения :
-(4x1 + 4x2) = B
4x1 * 4x2 = C
-------------------
-4(x1 + x2) = -4 * 13/2 = -26 = B
16 * (x1 * x2) = 16 * 5/2 = 40 = C
Составим уравнение :
[tex]x^{2} -26x+40 = 0[/tex]
Ответ : x^2 - 26x + 40 = 0
Ответ:
[tex]2x^2-13x+5=0\\\\D=169-40=129\ \ ,\ \ x_1=\dfrac{13-\sqrt{129}}{4}\ \ ,\ \ x_2=\dfrac{13+\sqrt{129}}{4}\\\\\\4x_1=13-\sqrt{129}\ \ ,\ \ 4x_2=13+\sqrt{129}\\\\x^2+px+q=0\ \ \to \ \ \ \left\{\begin{array}{l}4x_1+4x_2=-p\\4x_1\cdot 4x_2=q\end{array}\right\ \ \left\{\begin{array}{l}-p=13-\sqrt{129}+13+\sqrt{129}\\q=13^2-129\end{array}\right\\\\\\\left\{\begin{array}{l}-p=26\\q=40\end{array}\right\ \ \left\{\begin{array}{ccc}p=-26\\q=40\end{array}\right\\\\\\x^2-26x+40=0[/tex]