Question

If x=c√b+4 find x +1/x

Answer 1

1/x
= 1/(c√b + 4)
= (c√b - 4)/(c√b - 4) x 1/(c√b + 4)
= (c√b - 4)/(c2b - 16)

So, x + 1/x
= (c√b + 4) + (c√b - 4)/(c2b - 16)
= (c3b√b + 17c√b - 68 + 14c2b)/(c2b - 16)

Answer 2

Answer:

$x+\frac{1}{x}=\frac{c^2b+8c\sqrt{b}+17}{c\sqrt{b}+4}$

Step-by-step explanation:

We are given that, $x=c\sqrt{b}+4$

It is required to find the value of $x+\frac{1}{x}$

As we have, $x=c\sqrt{b}+4$

Then, $\frac{1}{x}=\frac{1}{(c\sqrt{b}+4)}$

Thus, we get,

$x+\frac{1}{x}=(c\sqrt{b}+4)+\frac{1}{(c\sqrt{b}+4)}$

i.e. $x+\frac{1}{x}=\frac{c\sqrt{b}+4)^2+1}{c\sqrt{b}+4}$

i.e. $x+\frac{1}{x}=\frac{c^2b+16+8c\sqrt{b}+1}{c\sqrt{b}+4}$

i.e. $x+\frac{1}{x}=\frac{c^2b+8c\sqrt{b}+17}{c\sqrt{b}+4}$

Hence, the value of $x+\frac{1}{x}=\frac{c^2b+8c\sqrt{b}+17}{c\sqrt{b}+4}$.