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Alona [7]
2 years ago
14

HELP!!

Mathematics
2 answers:
oksano4ka [1.4K]2 years ago
6 0

\qquad \qquad  \bf \huge\star \:  \:  \large{  \underline{Answer} }  \huge \:  \: \star

  • x + 1/x = 7

\textsf{  \underline{\underline{Steps to solve the problem} }:}

\qquad❖ \:  \sf \: {x}^{2}  +  \cfrac{1}{  {x}^{2} }  = 47

\qquad❖ \:  \sf \: {x}^{2}  +  \cfrac{1}{  {x}^{2} } + 2 - 2  = 47

( adding and subtracting 2, doesn't change the value )

\qquad❖ \:  \sf \: {x}^{2}  +  \cfrac{1}{  {x}^{2} } + 2  = 47 + 2

\qquad❖ \:  \sf \: {x}^{2}  +  \cfrac{1}{  {x}^{2} } +  \bigg(2 \sdot x \sdot \cfrac{1}{x}  \bigg)  = 49

( x cancel out, so no change in value )

\qquad❖ \:  \sf \: \bigg(x +  \cfrac{1}{x}  \bigg) {}^{2}  = 49

( use identity a² + 2ab + b² = (a + b)² )

\qquad❖ \:  \sf \: \bigg(x +  \cfrac{1}{x}  \bigg) {}^{}  =  \sqrt{49}

\qquad❖ \:  \sf \: x +  \cfrac{1}{x}  {}^{}  =  \pm7

since we have to take positive value, i.e greater than 0

\qquad❖ \:  \sf \: x +  \cfrac{1}{x}  {}^{}  =   7

\qquad \large \sf {Conclusion}  :

Therefore, the required value is 7

VMariaS [17]2 years ago
4 0

Answer:

  • x+\cfrac{1}{x} =7

================

<h3>Given:</h3>

  • x^2+\cfrac{1}{x^2} =47

Add 2 to both sides of equation:

  • x^2+\cfrac{1}{x^2}+2 =47+2

Then follow the steps:

  • x^2+\cfrac{1}{x^2}+2*x*\cfrac{1}{x} =49
  • (x+\cfrac{1}{x})^2=7^2

Take square root of both sides to get:

  • x+\cfrac{1}{x} =\pm\ 7

We are taking the positive value as we are told x > 0, hence the answer is 7.

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