Math, asked by basantiminin97, 1 month ago

Weckshet
Mathematics.
1. If x+1/x= 4, then find the value of x²+1/x²​

Answers

Answered by amansharma264
8

EXPLANATION.

⇒ (x + 1/x) = 4.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (4)².

⇒ x² + 1/x² + 2(x)(1/x) = 16.

⇒ x² + 1/x² + 2 = 16.

⇒ x² + 1/x² = 16 - 2.

⇒ x² + 1/x² = 14.

Answered by BrainlyArnab
1

 \huge \sf\red{ {x}^{2}  +  \frac{1}{  {x}^{2}  }  = 14}

Step-by-step explanation:

x +  \frac{1}{x}  = 4 \\  \\  =  >  {(x +  \frac{1}{x} )}^{2}  = ( {4)}^{2} ..(squaring \: both \: sides) \\  \\  =  >  {x}^{2}  + 2( \cancel{x })( \frac{1}{ \cancel{x} }) +  (\frac{1}{ { x} }  {)}^{2}  = 16 \\  \\  \{by \: the \: formula \: ( {a + b)}^{2}  =  {a}^{2}  + 2ab +  {b}^{2}  \} \\  =  >  {x}^{2}  +  \frac{1}{ {x}^{2} }  + 2 = 16 \\  \\    =  >  {x}^{2}  +  \frac{1}{ {x}^{2} }  = 16 - 2 \\  \\  \red{ {x}^{2}  +  \frac{1}{ {x}^{2} }  = 14}

Hence the value of + 1/ = 14.

hope it helps.

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