Math, asked by Shridharraman2006, 5 months ago

If X2 +1/x2 =14 then find the positive value of x+1/x​


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Answers

Answered by Darkrai14
7

4

Step-by-step explanation:

\rm x^2 + \dfrac{1}{x^2} = 14

\rm \Bigg ( x+\dfrac{1}{x}\Bigg )^2 = x^2+\dfrac{1}{x^2} + 2 \times x \times \dfrac{1}{x}

\rm \dashrightarrow\Bigg ( x+\dfrac{1}{x}\Bigg )^2 = 14 + 2

\rm \dashrightarrow\Bigg ( x+\dfrac{1}{x}\Bigg )^2 = 16

\rm \dashrightarrow x+\dfrac{1}{x}= \pm\sqrt{16}

Since Question is stating only postive value,

\bf\dashrightarrow x+\dfrac{1}{x}= 4

Answered by XxItzAnvayaXx
3

FINAL ANSWER:

(x^{2}-4x+1)(x^{2}+4x+1)

or

x^{4}-14x^{2}+1

QUESTION:

x^{2} + \frac{1}{x^{2}}=14

TO FIND:

value of x+\frac{1}{x}

SOLUTION:

x^{2} + \frac{1}{x^{2}}=14\\\frac{x^{2}(x^{2})+1}{x^{2}}=14\\{x^{2}(x^{2})+1}=14x^{2}\\x^{4}+1=14x^{2}\\\\x^{4}-14x^{2}+1=0\\(x^{2}-4x+1)(x^{2}+4x+1)

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