If x=-2 y=3 1/2 and z= 1/2 find the value of x+y+z/xyz
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Answered by
1
Answer:
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Answered by
1
Answer:
3
Explanation:
What I am going to use is the simple arithmetic geometric inequality.
(a1+a2+a3+……….+an)/n>=(a1.a2.a3………an)^(1/n)……(A)
Suppose question is
(a1+a2+a3+…an)=(a1.a2.a3.a4……an)
By equation (A)
(a1+a2+a3+…an)=((a1+a2+a3+….+an)/n)^(1/n)
Let ((a1+a2+a3+…an)=a
Then we can write
a=(a/n)^(1/n)
Or a^(n-1)=n^n
(a1+ ka+a3+…=n+an)=n^(n/(n-1))=n.n(1/(n-1))=(n^(1/n-1))^n=(a1.a2.a3…..an)
If we observe the above expression carefully the we got the solution.It seems that all value all equal to n^(1/(n-1)).Just check it.
For the question
x+y+z=x.y.z
n=3 So solution will be
x=y=z=3^(1/(3–1))=3^1/2=√3
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