A 1)1/√(a-1) +1/√(a+1)=(√(a+1)+√(a-1)))/√(a²-1) 2)(√(a+1)+√(a-1)))/√(a²-1) *√(a²-1)/(√(a-1)-√(a+1))= =(√(a+1)+√(a-1)))/(√(a-1)-√(a+1))= =(√(a+1)+√(a-1)))²/(√(a-1)-√(a+1)(√(a-1)+√(a+1)= =a+1+2√(a²-1)+a-1)/(a-1-a-1)=(2a+2√(a²-1))/(-2)=-a-√(a²-1) теперь подставим=(b²+c²)/2bc
Answers & Comments
Verified answer
548. a)a -1 = (b² +c² )/2bc - 1 = ( b² +c²-2bc) / 2bc =(b-c)² /2bc⇒√(a -1) = (b-c) /√(2bc).
* * * √(a -1) =√(b-c)² /2bc = |b-c| /√(2bc) = (b-c) /√(2bc , т. к. b>c * * *
a+1 = (b² +c² )/2bc +1 = ( b² +c²+2bc) /2bc=(b+c)² /2bc⇒√(a+1) = (b+c)/√(2bc).
-------
(1/√(a-1) +1/√(a+1) )* √(a² -1) / (√(a-1) - √(a+1) =
( √(a-1) +√(a+1) ) / (√(a-1) - √(a+1) ) = ( (b-c) /√(2bc) +(b+c)/√(2bc) ) /
( (b-c) /√(2bc) -(b+c)/√(2bc) ) = 2b / (-2c) = -b/c .
---------------------------------------
548. б)
x =(1/2) *(√(a/b) + √(b/a) ) =(a+b) /2√(ab)
x² - 1 = ( (a+b) /2√(a*b) )² -1 = ( (a+b)² / (4a*b) -1 ) = ( (a - b)² / (4ab)
√(x² - 1) = (a-b) / 2√(ab)
-------
2b√(x² -1) / (x - √(x² -1) = 2b √(x² -1) * ( x + √(x² -1) = 2b (a-b) / 2√(ab *
( (a+b) /2√(ab) + (a-b) / 2√(ab ) = b (a - b) / √(ab * a / √(ab = a -b .
Verified answer
A1)1/√(a-1) +1/√(a+1)=(√(a+1)+√(a-1)))/√(a²-1)
2)(√(a+1)+√(a-1)))/√(a²-1) *√(a²-1)/(√(a-1)-√(a+1))=
=(√(a+1)+√(a-1)))/(√(a-1)-√(a+1))=
=(√(a+1)+√(a-1)))²/(√(a-1)-√(a+1)(√(a-1)+√(a+1)=
=a+1+2√(a²-1)+a-1)/(a-1-a-1)=(2a+2√(a²-1))/(-2)=-a-√(a²-1)
теперь подставим=(b²+c²)/2bc
б смотреть во вложении