Question

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Answer 1

Answer:

18

Step-by-step explanation:

⇒ x^2 - 4x = 1

⇒ x^2 - 1 = 4x

⇒ ( x^2 - 1 ) / x = 4

⇒ x - 1 / x = 4

       Square on both sides:

⇒ ( x - 1 / x )^2 = 4^2

⇒ x^2 + 1 / x^2 - 2( x * 1 / x ) = 16

⇒ x^2 + 1 / x^2 - 2( 1 ) = 16

⇒ x^2 + 1 / x^2 - 2 = 16

⇒ x^2 + 1 / x^2 = 16 + 2 = 18

Answer 2

$\huge\sf\red{Answer:}$

★ Given:

⇒ $\sf x^2 - 4x = 1$

★ Find:

⇒ $\sf x^2 + \dfrac{1}{x^2}$

★ Calculations:

⇒ $\sf x^2 - 4x = 1$

⇒ $\sf x^2 - 1 = 4x$

⇒ $\sf \dfrac{(x^2 - 1)}{x} = 4$

⇒ $\sf \dfrac{x - 1}{x} = 4$

★ Squaring both the sides:

⇒ $\sf \dfrac{(x - 1}{x)}^2 = 4^2$

⇒ $\sf \dfrac{x^2 + 1}{x^2} - 2( \dfrac{x \times 1}{x}) = 16$

⇒ $\sf \dfrac{x^2 + 1}{x^2 - 2 \: (1)}= 16$

⇒ $\sf \dfrac{x^2 + 1}{x^2 - 2} = 16$

⇒ ${\sf{\underline{\boxed{\green{\sf{\dfrac{x^2 + 1}{x^2 = 16 + 2} = 18}}}}}}$

Therefore, 18 is the answer.