Question

x^2+1/x^2=18,find the value x-1/x​

Answer 1

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➠  $x^{2} + \dfrac{1}{x^2} = 18 \; , \mathtt { then \; find \; value \; of } \;x - \dfrac{1}{x}$

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$\underline{\boxed{\bold{ \bigstar \; Important \; Information \; \bigstar }}}$  

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❏ Algebraic identities that are frequently used in mathematics to simply our calculations and get our answer in short period of time.  

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❏ Here are some important identities used in daily mathematics.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{\orange {:\longmapsto \; (a+b)^2 = a^2 + b^2 + 2ab}}$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{\pink {:\longmapsto \; (a-b)^2 = a^2 + b^2 - 2ab}}$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{\orange {:\longmapsto \; a^2-b^2 = (a+b)(a-b) }}$

$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{\pink {:\longmapsto \; x+a)(x+b) = x^2 + (a+b)x+ab}}$

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➠  $x^{2} + \dfrac{1}{x^2} = 18$

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Let's Start !

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Let's use second identity !

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed{\red {:\longmapsto \; (x-\dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} - 2(x)(\dfrac{1}{x} ) }}$

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$:\implies \; (x-\dfrac{1}{x})^2 = x^2 + \dfrac{1}{x^2} - 2$

$:\implies \; (x-\dfrac{1}{x})^2 = 18 - 2$

$:\implies \; (x-\dfrac{1}{x})^2 = 16$

$:\implies \; \sqrt {(x-\dfrac{1}{x})^2 } = \sqrt{ 16}$

$:\implies \; (x-\dfrac{1}{x}) = \sqrt{ 16}$

$\green {: \implies \; (x-\dfrac{1}{x}) = \pm 4 }$

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$\boxed{\boxed{\bold{\therefore Value \; of \; (x-\dfrac{1}{x}) = \pm 4 }}}$

 

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Hope this helps u.../

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