Question

(x^2+x+3)*(x^2+x+8)=50

Answer 1

(x^2+x+3)*(x^2+x+8)=50
x^2+x+3=y
y*(y+5)=50
y^2+5y-50=0
D=225
y1=-10
y2=5
1) x^2+x+3=-10
D=1-4*13  <0
нет решений
2)x^2+x+3=5
x^2+x-2=0
D=9
x1=-2
x2=1
ответ :
x1=-2
x2=1

Answer 2

To solve the equation ${(x^2+x+3)(x^2+x+8) = 50}$, we can expand the product on the left side of the equation and then simplify it to a quadratic equation. Let's proceed with the steps:

Expand the left side: $x^2(x^2+x+8) + x(x^2+x+8) + 3(x^2+x+8) = 50$

Simplify: $x^4 + x^3 + 8x^2 + x^3 + x^2 + 8x + 3x^2 + 3x + 24 = 50$

Combine like terms: $x^4 + 2x^3 + 12x^2 + 11x + 24 = 50$

Rearrange the equation: $x^4 + 2x^3 + 12x^2 + 11x + 24 - 50 = 0$

Simplify further: $x^4 + 2x^3 + 12x^2 + 11x - 26 = 0$

Unfortunately, this equation cannot be solved algebraically using elementary methods. You'll need to use numerical methods or a graphing calculator to approximate the solutions.