If f(2 x)=4 x^2+1 , then for how many real values of x will f(2 x) be the GM of f(x) and f(4 x) ?

Step-by-step solution

Given aligned & f(2 x)=4 x^2+1 f(x)=x^2+1 & f(4 x)=16 x^2+1 & (f(2 x))^2=f(x) f(4 x) & (4 x^2+1 )^2= (x^2+1 ) (16 x^2+1 ) & (f(2 x) is G M of f(x) & f(4 x)) & 16 x^4+1+8 x^2=16 x^2+16 x^2+1+x^2 & 9 x^2=0 & x=0 aligned One real value of x is possible.