Question

(2b кор(x^2-1))/(x-кор(x^2-1)) если х=0.5(кор(а/b)+кор(b/a)) ; a>0;b>0;a>b.

Answer 1

x=(a+b)/(2sqrt(ab))

x^2=(a+b)^2/4ab

2bsqrt(x^2-1)=2bsqrt((a-b)^2/4ab)=(a-b)/sqrt(a/b)

x-sqrt(x^2-1)=((2b кор(x^2-1))/(x-кор(x^2-1)) a+b)/(2sqrt(ab))-(a-b)/2sqrt(ab)=2b/2sqrt(ab)=1/sqrt(a/b)

[(a-b)/sqrt(a/b)]/[1/sqrt(a/b)]=a-b