Question

If f(x^2 + 2 + 1/x^2) = x^2 - 2 + 1/x^2, then f(5) is.

Answer 1

Answer:

1

Step-by-step explanation:

$f[x^{2} +2+\frac{1}{x^{2} } ]=x^{2} -2+\frac{1}{x^{2} }$

$[x^{2} +2+\frac{1}{x^{2} }]= (x+\frac{1}{x} )^{2}$

putting$(x+\frac{1}{x} )^{2}=5$

$[x+\frac{1}{x} ]=\sqrt{5}$

Therefore after solving for x we get,

$x=\frac{-\sqrt{5}+1 }{2}$

now putting the value for x in$x^{2}-2+\frac{1}{x^{2} }$ we get value as 1

therefore f(5)=1