已知根号a-根号a=根号5,求下列各式的值（1）a的1//2次+a-1/2次（2）(a3/2+a-3/2)/(a1/2+a-1/2)题目错了事根号a-1/根号a=根号5

Question

已知根号a-根号a=根号5,求下列各式的值（1）a的1//2次+a-1/2次 （2）(a3/2+a-3/2)/(a1/2+a-1/2)
题目错了事根号a-1/根号a=根号5

Answer 1

√a-1/√a=√5;
(1)√a+1/√a=√(√a-1/√a)²+4=√(5+4)=3;
(2)(a√a+1/a√a)(√a+1/√a)
=a²+a+1/a+1/a²
=(a+1/a)²-2+(a+1/a)
=[(√a+1/√a)²-2]²-2+(√a+1/√a)²-2
=(3-2)²-2+3²-2
=1-2+9-2
=6;
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