Question

Упростить: $|-b| sqrt{b^2-2+ frac{1}{b^2} }$, если 0<b<1.

Answer 1

$|-b| sqrt{b^2-2+ frac{1}{b^2} } = b sqrt{(b- frac{1}{b} )^2} = b|b- frac{1}{b} | = \ = b| frac{b^2-1}{b} | ( frac{b^2-1}{b} textless 0) = b * (- frac{b^2-1}{b} ) = -(b^2-1)=1-b^2$