Math, asked by Boonsai1393, 1 year ago

If x^2+1/x^2=34 find x^3+1/x^3

Answers

Answered by vibhakurup
0

Hope this helps you, if you have any doubt please comment

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Answered by LovelyG
9

Answer:

198

Step-by-step explanation:

Given that;

 \tt {x}^{2}  +  \dfrac{1}{ {x}^{2} }  = 34

On adding 2 both sides ;

 \tt x^{2}  +  \frac{1}{ {x}^{2}} + 2 = 34 + 2 \\  \\ \tt  {x}^{2}  +  \frac{1}{ {x}^{2} }  + 2 \: . \: x \: . \:  \frac{1}{x}  = 36 \\  \\ \tt (x +  \frac{1}{x} )^{2}  = 36 \\  \\ \tt x +  \frac{1}{x}  =  \pm \sqrt{36}  \\  \\ \tt x +  \frac{1}{x}  = 6 \:  \: (taking \: positive \: value)

Now, on cubing both sides ;

\rightarrow \tt \left( x +  \frac{1}{x} \right)^{3}  = (6) {}^{3}  \\  \\  \tt  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 3(x +  \frac{1}{x} ) = 216 \\  \\ \tt  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 3 \times 6 = 216 \\  \\ \tt  {x}^{3}  +  \frac{1}{ {x}^{3} }  + 18 = 216 \\  \\ \tt  {x}^{3}  +  \frac{1}{ {x}^{3} }  = 216 - 18 \\  \\ \tt  {x}^{3}  +  \frac{1}{ {x}^{3} }  = 198

Hence, the answer is 198.

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