Question

Упростите выражение,если 1≤b≤2 $sqrt{(2- sqrt{b}) ^{2}+8 sqrt{b}}- sqrt{(1+ sqrt{b}) ^{2} -4 sqrt{b}$

Answer 1

$sqrt{(2- sqrt{b})^2+8 sqrt{b} }- sqrt{(1+ sqrt{b})^2-4 sqrt{b} }= \ = sqrt{2^2-2*2* sqrt{b} +(sqrt{b})^2+8 sqrt{b} }- sqrt{1^2+2*1* sqrt{b} + (sqrt{b})^2-4 sqrt{b} } \ =sqrt{2^2-4 sqrt{b} +(sqrt{b})^2+8 sqrt{b} }- sqrt{1^2+2 sqrt{b} + (sqrt{b})^2-4 sqrt{b} } = \ =sqrt{2^2+4 sqrt{b} +(sqrt{b})^2 }- sqrt{1^2-2 sqrt{b} + (sqrt{b})^2 } = \ = sqrt{(2+ sqrt{b})^2 }- sqrt{(1-sqrt{b})^2 }=|2+ sqrt{b}|-|1-sqrt{b}|= \ =2+ sqrt{b}-(sqrt{b}-1)=3$