Question

(x² -6x+3)(x²−6x+4) = 2​

Answer 1

(x² -6x+3)(x²−6x+4) = 2​

x² -6x+3 = t

t(t + 1) = 2

t² + t - 2 = 0

D = 1 + 8 = 9

t₁₂ = (-1 +- 3)/2 = 1    -2

1/ t = 1

x² -6x+3 = 1

x² -6x+2 = 0

D = 36 - 8 = 28

x₁₂ = (6 +- √28)/2 = 3 +- √7

2/ t = -2

x² -6x+3 = -2

x² -6x+5 = 0

D = 36 - 20 = 16

x₃₄ = (6 +- 4)/2 = 5    1

ответ х = {1, 5,  3 - √7 ,3 + √7}

Answer 2

Решение к заданию на фото. По формуле Герона.

Ответы: x1 = 3+√7

x2 = 3–√7

x3 = 5

x4 = 1

Answer 3

To solve the equation $(x^2 - 6x + 3)(x^2 - 6x + 4) = 2$, you can start by expanding the left side of the equation and then rearranging it to isolate (x:

$(x^2 - 6x + 3)(x^2 - 6x + 4) = 2$

First, expand the left side of the equation:

$x^4 - 6x^3 + 3x^2 - 6x^3 + 36x^2 - 18x + 4x^2 - 24x + 12 = 2$

Now, combine like terms:

$x^4 - 12x^3 + 43x^2 - 42x + 12 = 2$

Subtract 2 from both sides of the equation to isolate the polynomial on the left side:

$x^4 - 12x^3 + 43x^2 - 42x + 10 = 0$

Unfortunately, this is a quartic equation (an equation of degree 4), and there's no general formula to solve quartic equations. However, you can use numerical methods or software to find approximate solutions. You can also try factoring it or using other algebraic techniques, but this particular quartic equation doesn't appear to have simple, factorable solutions.