Question

if x^2 +(4/x^2)=5 find the value of x^3+(8/x^3)
answer this question... ​

Answer 1

Answer:

9

Step-by-step explanation:

The Given Equation is:

      $x^{2} +\frac{4}{x^{2} } =5$

Or, $x^{2} +\frac{2^{2} }{x^{2} } =5$

Or, $(x)^{2} +(\frac{2}{x })^{2} =5$

Or, $(x+\frac{2}{x} )^{2} -2*x*\frac{2}{x} = 5$      $[a^{2} +b^{2} =(a+b)^{2} -2ab]$

Or, $(x+\frac{2}{x} )^{2} -4 = 5$

Or, $(x+\frac{2}{x} )^{2} = 5+4$

Or, $(x+\frac{2}{x} )^{2} = 9$

Or, $(x+\frac{2}{x} )^{2} = 3^{2}$

Or, $x+\frac{2}{x} =3$

The Given Statement is:

  $x^{3} + \frac{8}{x^{3} }$

= $x^{3} + \frac{2^{3} }{x^{3} }$

= $(x)^{3} +(\frac{2}{x}) ^{3}$

= $(x+\frac{2}{x} )^{3} -3*x*\frac{2}{x} * (x+\frac{2}{x} )$     $[(a+b )^{3} -3ab(a+b )]$

= $(x+\frac{2}{x} )^{3} -6 (x+\frac{2}{x} )$

= $3^{3} -6* 3$      $[x+\frac{2}{x} =3]$

= $27-18$

= $9$   (ans)

Hope you understand the process...

By- Md. Mominur Islam Mahim.