a fost răspuns

Rezolvati in multimea numerelor reale ecuatia:
|x-2|+|2x-4|+|3x-6|+...+|20x-40|=420

Răspuns :

Răspuns:

0; 4.

Explicație pas cu pas:

|x-2|+|2x-4|+|3x-6|+...+|20x-40|=420, ⇒ |x-2|+|2(x-2)|+|3(x-2)|+...+|20(x-2)|=420, ⇒1·|x-2|+2·|x-2|+3·|x-2|+...+20·|x-2|=420, ⇒|x-2|·(1+2+3+...+20)=420, ⇒|x-2|·(1+20)·20/2=420, ⇒|x-2|·21·10=420, ⇒|x-2|=420:210, ⇒|x-2|=2, ⇒

x-2=-2  sau  x-2=2, ⇒ x=0  sau x=4.