The product of all the values of a, such that f(a)=f(2a) is -1/2
Functions and expressions
Given the function below;
f(x)=1/x + x
f(a) = 1/a + a
f(2a) = 1/2a + 2a
If f(a) = f(2a), hence;
1/a + a = 1/2a + 2a
Collect the like terms
1/a - 1/2a = 2a - a
2-1/2a = a
1/2a = a
Cross multiply
2a² = 1
a² = 1/2
a = ±√1/2
The values of a are √1/2 and -√1/2
Product = -√1/2 * √1/2
Product = -1/2
Hence the product of all the values of a, such that f(a)=f(2a) is -1/2
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