Toán nâng cao đại số 8

V

vipboycodon

Câu 1:
$(x-2012)^3+(x-2014)^3 = (2x-4026)^3$ (*)

Đặt $x-2012 = a$ , $x-2014 = b$

(*) $\rightarrow a^3+b^3 = (a+b)^3$

$\leftrightarrow a^3+b^3 = a^3+3a^2b+3ab^2+b^3$

$\leftrightarrow ab(a+b) = 0$

$\leftrightarrow \left[\begin{matrix} a = 0 \\ b = 0 \\ a+b = 0 \end{matrix}\right.$ $\rightarrow \left[\begin{matrix} x = 2012 \\ x = 2014 \\ x = 201\end{matrix}\right.$

Câu 2:
$(x-3)^4+(x-5)^4 = 16$ (*) (*)

Đặt $x-4 = t $

(*) (*) $\rightarrow (t+1)^4+(t-1)^4 = 16$

$\leftrightarrow t^4+4t^3+6t^2+4t+1+t^4-4t^3+6t^2-4t+1 = 16$

$\leftrightarrow 2t^4+12t^2-14 = 0$

$\leftrightarrow 2(t^2-1)(t^2+7) = 0$

$\leftrightarrow \begin{cases} t = 1 \\ t = -1 \end{cases}$ $\rightarrow \begin{cases} x = 5 \\ x = 3 \end{cases}$
 
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