Question

(x^2+x)^2-5(x^2+x)+6=0

Answer 1

Делаем замену:
y=x^2+x
получим:
y^2-5y+6=0
D=25-24=1
y1=(5+1)/2=3
y2=(5-1)/2=2
обратная замена:
x^2+x=2
x^2+x-2=0
D=1+8=9
x1=(-1+3)/2=1
x2=-4/2=-2
x^2+x=3
x^2+x-3=0
D=1+12=13
x3=(-1+sqrt(13))/2
x4=(-1-sqrt(13))/2
Ответ: x1=1; x2=-2; x3=(-1+sqrt(13))/2; x4=(-1-sqrt(13))/2

Answer 2

Solving the Equation

The given equation is (x^2+x)^2-5(x^2+x)+6=0. Let's solve it step by step.

Step 1: Simplify the equation by expanding and combining like terms.

(x^2+x)^2-5(x^2+x)+6=0

Expanding the first term: (x^2+x)^2 = (x^2+x)(x^2+x) = x^4 + 2x^3 + x^2

Expanding the second term: -5(x^2+x) = -5x^2 - 5x

Combining the terms: x^4 + 2x^3 + x^2 - 5x^2 - 5x + 6 = 0

Simplifying further: x^4 + 2x^3 - 4x^2 - 5x + 6 = 0.

Step 2: Solve the equation.

Unfortunately, the equation x^4 + 2x^3 - 4x^2 - 5x + 6 = 0 does not have a simple algebraic solution. It is a quartic equation, which means it is a polynomial equation of degree 4. Solving quartic equations can be complex and often requires numerical methods or factoring techniques.

Without further information or constraints, it is not possible to determine the exact values of x that satisfy the equation.

Please let me know if there is anything else I can help you with!