Math, asked by qsattar18, 9 months ago


ifx +  \frac{1}{x}  = 5 find x3 +  \frac{1}{x3}

Answers

Answered by tahseen619
0

Answer:

I think Answer is 2525 .

Step-by-step explanation:

x +  \frac{1}{x}  = 5 \\   (x +  \frac{1}{x}  ) ^{2}  =  {5}^{2}  \\  {x}^{2}  +  \frac{1}{ {x}^{2} } +   2.x. \frac{1}{x}  = 25 \\  {x}^{2}  +  \frac{1}{ {x}^{2} }  = 25 - 2 = 23 \\  \\ x +  \frac{1}{x}  = 5 \\  {(x +  \frac{1}{x}) }^{3} =   {5}^{3}  \\  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 3.x. \frac{1}{x} (x +  \frac{1}{x} ) = 125 \\  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 3(5) = 125 \\  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 15 = 125 \\  {x}^{3}  +  \frac{1}{ {x}^{3} }  = 110

( {x}^{2}  +   \frac{1}{ {x}^{2} } )( {x}^{3}  +  \frac{1}{ {x}^{3} } ) = 110 \times 23 \\  {x}^{5}  +  \frac{1}{ {x}^{5} }  + x +  \frac{1}{x}  = 2530 \\  {x}^{5}  +  \frac{1}{ {x}^{5} }  + 5 = 2530 \\  {x}^{5}  +  \frac{1}{ {x}^{5} }  = 2525

Answered by sudhakask
0

THE ANSWER HAD BEEN SOLVED BEFORE ME

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