Question

Determinati multimea B = { x ∈ R | \sqrt{9x^{2} -6x+1} = 4} .

Answer 1

Răspuns:

B={-1; 5/3}

Explicație pas cu pas:

$\sqrt{9x^{2}-6x+1}=\sqrt{(3x)^{2}-2*3x*1+1^{2}}=\sqrt{(3x-1)^{2}} =|3x-1|\\ Deci~|3x-1|=4,~3x-1=-4~sau~3x-1=4\\3x=-3,~sau~3x=5\\x=-1~sau~x=\frac{5}{3}$

Deci B={-1; 5/3}