Question

x+1/x =14 then x√x-14 = ?x+1/x=14 then x√x-14 =?

Answer 1

$\sqrt{x}$ + $\frac{1}{\sqrt{x} }$ = 4

Step-by-step explanation:

Given,

x + $\frac{1}{x}$ = 14   .... (1)

$[tex]\sqrt{x}$ + $\frac{1}{\sqrt{x} }$^{2}[/tex] = x + $\frac{1}{x}$ + 2

$[tex]\sqrt{x}$ + $\frac{1}{\sqrt{x} }$^{2}[/tex] = 14 + 2 = 14

∴ $\sqrt{x}$ + $\frac{1}{\sqrt{x} }$ = 4

Hence, $\sqrt{x}$ + $\frac{1}{\sqrt{x} }$ = 4.

Answer 2

Step-by-step explanation:

1. $\sqrt{x } + \frac{1}{\sqrt{ x} } = 4$
2. $( \sqrt{x} + \frac{1}{ \sqrt{} x} )^{3} = 4 {}^{3}$
3. $\sqrt[x]{x} + \frac{1}{ \sqrt[x]{x} } = 52........(1)$
4. then
5. $\sqrt[]{x} - \frac{1}{ \sqrt[]{x} } = \sqrt{14 - 2} = 2 \sqrt{3}$
6. and
7. $\sqrt[x]{x} - \frac{1}{ \sqrt[x]{x} } = 30 \sqrt{3} .........(2)$
8. add(1+2), then
9. $2x \sqrt{x} = 52 + 30 \sqrt{3}$
10. $x \sqrt{x} - 14 = 26 + 15 \sqrt{3} - 14$
11. $= 12 + 15 \sqrt{3}$
12. $= 3(4 + 5 \sqrt[]{3} ) \: ans..$