Question

$\sqrt{4m^{2} - 4m + 1 } + |1 - 2m| \leqslant 2$
Cum se rezolvă? AJUTOR, vă rog!

Answer 1

√4m²-4m+1 +|1-2m| <= 2 <=> |2m-1| +|1-2m| <= 2;

Daca m=0 => |-1|+|1| <= 2 <=> 2 <= 2 ,care este adevarat deci este solutie.

Daca m > 1/2 => 2m-1+2m-1 <= 2 <=> 4m-2 <= 2 <=> m <= 1 => m∈(1/2,1] deci este solutie.

Daca m < 1/2 => 1-2m+1-2m <= 2 <=> 2-4m <= 2 <=> m >= 0 => m∈[0,1/2) deci este solutie.

Daca m=1/2 => 0+0=0 <= 2, care este evident adevarat.

In concluzie, S=[0,1].

Answer 2

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