Hằng đẳng thức( 3 cái đầu)

P

pinkylun

ta có:

$a+b=c+d=>a-c=d-b$

$a^2+b^2=c^2+d^2$

$<=>a^2-c^2=d^2-b^2$

$<=>(a-c)(a+b)=(d-b)(d+b)$

hay $(a-c)(c+d)=(a-c)(d+b)$

$<=>(a-c)(c+d)-(a-c)(d+b)=0$

$<=>(a-c)(c-b)=0$

$<=>a=c$ hay $c=b$

TH1: $<=>a=c$ mà $a+b=c+d=>b=d=>b^{2015}=d^{2015}$

$a=c=>a^{2015}=c^{2015}$

$=>a^{2015}+b^{2015}=c^{2015}+d^{2015}$

TH2: $c=b$ mà $a+b=c+d=>a=d=>a^{2015}=d^{2015}$

$c=b=>c^{2015}=b^{2015}$

$=>a^{2015}+b^{2015}=d^{2015}+c^{2015}$
 
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