SOLUTION: Given a=x(^1/2)- 4x(^-1/2). What is the value of 1/a^-2??? I think the answer is x^2-8x+16/x , can someone please confirm ????

Question 132889: Given a=x(^1/2)- 4x(^-1/2). What is the value of 1/a^-2??? I think the answer is x^2-8x+16/x , can someone please confirm ????
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a=x(^1/2)- 4x^(-1/2) I assume that this is the problem.
4x^(-1/2)=4/sqrt(x) since only x is taken to the -1/2 power.
1/a^-2=a^2
a^2=(sqrt(x)-4/sqrt(x))^2
=x-8+ 16/x
You were almost correct the -8 doesn't have an x after it and the x isn't squared.
sqrt(x)* -4/sqrt(x)=-4sqrt(x)/sqrt(x)=-4
sqrt(x)^2=x
.
Ed

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