Question

Упростите выражение $sqrt{4x^{2} - 4x+1}$ , если а)x<0,5 б)x ≥0,5

Answer 1

$4x^2-4x+1=4(x^2-x)+1=4(, (x-frac{1}{2})^2-frac{1}{4}, )+1=\\=4(x-frac{1}{2})^2-1+1=4(x-frac{1}{2})^2=4(x-0,5)^2\\a); ; x textless 0,5; ; to ; (x-0,5) textless 0\\sqrt{4x^2-x+1}=sqrt{4(x-0,5)^2}=2cdot |x-0,5|=2cdot (0,5-x)=1-2x\\b); ; x geq 0,5; ; to ; ; (x-0,5) geq 0\\sqrt{4x^2-4x+1}=sqrt{4(x-0,5)^2}=2cdot |x-0,5|=2(x-0,5)=2x-1$

Answer 2

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