Question

if x-1/x=7 then what is the value of x2+1/x2​

Answer 1

Answer:

x²+1/x² = 51

Explanation:

Given x - 1/x = 7 ---(1)

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We know the algebraic identity:

a²+b²-2ab = (a-b)²

Or

a²+b² = (a-b)²+2ab

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Now,

x²+1/x²

= (x-1/x)²+2*x*(1/x)

= (x-1/x)²+2

= 7²+2 [ from (1)]

= 49+2

= 51

Therefore,

x²+1/x² = 51

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Answer 2

Given,

$\huge \boxed{ \rm{}x - \frac{1}{x} = 7}$

• To find : $\sf{x}^{2} + \frac{1}{ {x}^{2} }$

Here,

$\mapsto \: \bf{x - \frac{1}{x} = 7 }$

• Squaring both sides,

$\to \: \bf {\bigg(x - \frac{1}{x} \bigg)}^{2} = {(7)}^{2}$

$\texttt{We know, }\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \bullet \: \purple{{(a - b)}^{2} } = \pink{ {a}^{2} + {b}^{2} - 2ab}$

• Here, LHS is in form of above (tagged) identity. So, applying this identity, we get,

$\to \bf{x}^{2} + \frac{1}{ {x}^{2} } - 2(\cancel{x}) \bigg( \frac{1}{ \cancel{x}} \bigg) = 49$

$\to \bf {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 49 \\ \\ \to \bf \: \: \: \: \: \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 49 +2 \\ \\ \to \bf\: \: \: \: \: \: \: {x}^{2} + \frac{1}{ {x}^{2} } = \red{51}$

Hence,

• Required value of $\sf{{x}^{2} + \dfrac{1}{ {x}^{2} } \: \: is \: \: \: \red{51} }.$