помогите плиз решить 6.256и6.254. Created by 1CheshireCat1. algebra-ru

помогите плиз решить 6.256и6.254...

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$(x+3)^4+(x+5)^4=16\\\\t=x+4\; \; \to \; \; \; x+3=t-1\; ,\; \; x+5=t+1\\\\(t-1)^4+(t+1)^4=16\\\\(t^4-4t^3+6t^2-4t+1)+(t^4+4t^3+6t^2+4t+1)=16\\\\2t^4+12t^2+2=16\\\\t^4+6t^2-7=0\\\\p=t^2 \geq 0\; ,\; \; p^2+6p-7=0\; ,\; p_1=-7\; ,\; \; p_2=1\; \; (teorema\; Vieta)\\\\p_1=-7\; \; ne\; podxodit\; ,\; t.k.\; \; p \geq 0\\\\p=1\; \;\Rightarrow \; \; t^2=1\; ,\; \; t_1=-1\; ,\; \; t_2=1\\\\a)\; \; x+4=-1\; \; \Rightarrow \; \; x=-5\\\\b)\; \; x+4=1\; \; \Rightarrow \; \; x=-3\\\\Otvet:\; \; x_1=-5\; ,\; \; x_2=-3$

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sedinalana (x+3)^4+(x+5)^4=2^4⇒
1){|x+3|=0⇒x=-3
{|x+5|=2⇒x+5=-2 U x+5=2⇒x=-7 U x=-3
x=-3
2){|x+3|=2⇒x+3=-2 U x+3=2⇒x=-5 U x=-1
{|x+5|=0⇒x=-5
x=-5
Ответ x=-3;x=-5

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