To solve the equation (х^2 + х + 4)^2 + 8х(х^2 + х + 4) +15х^2 = 0, let's expand it step by step:
First, expand (х^2 + х + 4)^2:
(х^2 + х + 4)^2 = (х^2 + х + 4)(х^2 + х + 4)= (х^2)(х^2) + (х^2)(х) + (х^2)(4) + (х)(х^2) + (х)(х) + (х)(4) + (4)(х^2) + (4)(х) + (4)(4)= х^4 + х^3 + 4х^2 + х^3 + х^2 + 4х + 4х^2 + 4x + 16= х^4 + 2х^3 + 9х^2 + 8х + 16
Next, expand 8х(х^2 + х + 4):
8х(х^2 + х + 4) = 8х(х^2) + 8х(х) + 8х(4)= 8х^3 + 8х^2 + 32х
Now, substitute the expansions back into the equation:
(х^4 + 2х^3 + 9х^2 + 8х + 16) + (8х^3 + 8х^2 + 32х) + 15x^2 = 0х^4 + 2х^3 + 9х^2 + 8х + 16 + 8х^3 + 8х^2 + 32х + 15x^2 = 0х^4 + 2х^3 + 8х^3 + 9х^2 + 8х^2 + 15x^2 + 8х + 32х + 16 = 0х^4 + 10х^3 + 32х^2 + 40x + 16 = 0
So, the simplified form of the given equation is х^4 + 10х^3 + 32х^2 + 40x + 16 = 0.
To solve the equation (х^2 + х + 4)^2 + 8х(х^2 + х + 4) +15х^2 = 0, let's expand it step by step:
First, expand (х^2 + х + 4)^2:
(х^2 + х + 4)^2 = (х^2 + х + 4)(х^2 + х + 4)
= (х^2)(х^2) + (х^2)(х) + (х^2)(4) + (х)(х^2) + (х)(х) + (х)(4) + (4)(х^2) + (4)(х) + (4)(4)
= х^4 + х^3 + 4х^2 + х^3 + х^2 + 4х + 4х^2 + 4x + 16
= х^4 + 2х^3 + 9х^2 + 8х + 16
Next, expand 8х(х^2 + х + 4):
8х(х^2 + х + 4) = 8х(х^2) + 8х(х) + 8х(4)
= 8х^3 + 8х^2 + 32х
Now, substitute the expansions back into the equation:
(х^4 + 2х^3 + 9х^2 + 8х + 16) + (8х^3 + 8х^2 + 32х) + 15x^2 = 0
х^4 + 2х^3 + 9х^2 + 8х + 16 + 8х^3 + 8х^2 + 32х + 15x^2 = 0
х^4 + 2х^3 + 8х^3 + 9х^2 + 8х^2 + 15x^2 + 8х + 32х + 16 = 0
х^4 + 10х^3 + 32х^2 + 40x + 16 = 0
So, the simplified form of the given equation is х^4 + 10х^3 + 32х^2 + 40x + 16 = 0.