Решите через теорема виета 1,2 номер. Created by Daniltitov1003. algebra-ru

Решите через теорема виета 1,2 номер...

drakerton

$1)\; \; x^2+15x+56=0\; \; ,\; \; \left \{ {{x_1\cdot x_2=56} \atop {x_1+x_2=-15}} \right.\; \; \to \; \; x_1=-7\; ,\; x_2=-8\\\\2)\; \; x^2-11x+28=0\; \; ,\; \; \left \{ {{x_1\cdot x_2=28} \atop {x_1+x_2=11}} \right.\; \; \to \; \; x_1=4\; ,\; x_2=7\\\\2)\; \; x^2-2x-35=0\; \; ,\; \; \left \{ {{x_1\cdot x_2=-35} \atop {x_1+x_2=2}} \right.\; \; \to \; \; x_1=-5\; ,\; x_2=7\\\\4)\; \; x^2+3x-54=0\; \; ,\; \; \left \{ {{x_1\cdot x_2=-54} \atop {x_1+x_2=-3}} \right.\; \; \to \; \; x_1=-9\; ,\; x_2=6$

$5)\; \; x_1=3\; ,\; x_2=-9\; \; ,\; \; \left \{ {{3\cdot (-9)=-27} \atop {3+(-9)=-6}} \right. \; \; \to \; \; x^2+6x-27=0$

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Verified answer

Задание 1

1. х² + 15х + 56 = 0

х₁ + х₂ = -15

х₁ · х₂ = 56

х₁ = -7

х₂ = -8

2. х² - 11х + 28 = 0

х₁ + х₂ = 11

х₁ · х₂ = 28

х₁ = 4

х₂ = 7

3. х² - 2х - 35 = 0

х₁ + х₂ = 2

х₁ · х₂ = -35

х₁ = 7

х₂ = -5

4. х² + 3х - 54 = 0

х₁ + х₂ = -3

х₁ · х₂ = -54

х₁ = 6

х₂ = -9

Задание 2

х₁ + х₂ = 3 + (-9) = 3 - 9 = -6

х₁ · х₂ = 3 · (-9) = -27

Наше уравнение:

х² + 6х - 27 = 0

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