Question

Answer me....pls...........​

Answer 1

Answer:

1. 14

2. -8√3

Step-by-step explanation:

please refer to the photo attached....

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Answer 2

x = 2 - √3

___________ [ GIVEN ]

• We have to find the value of x² + $\dfrac{1}{ {x}^{2} }$ and x² - $\dfrac{1}{ {x}^{2} }$

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• x = 2 - √3 ______ (eq 1)

• $\dfrac{1}{x}\:=\: \dfrac{1}{2 \: - \: \sqrt{3} }$

=> $\dfrac{1}{2 \: - \: \sqrt{3} } \: \times \: \dfrac{2 \: + \: 3}{2 \: + \: \sqrt{3} }$

We know that ..

(a - b) (a + b) = a² - b²

=> $\dfrac{2 \: + \: \sqrt{3}}{ {(2)}^{2} \: - \: (\sqrt{3})^{2} }$

=> $\dfrac{2 \: + \: \sqrt{3} }{ 4 \: - \: 3}$

=> $\dfrac{2 \: + \: \sqrt{3} }{ 1}$

=> 2 + √3 _____ (eq 2)

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Now..

• x + $\dfrac{1}{x}$ = 2 - √3 + 2 + √3

=> 4

Now.. squaring on both sides ..

=> $\bigg(x \: + \: \dfrac{1}{x} \bigg )^{2}$ = (4)²

=> x² + $\dfrac{1}{ {x}^{2} }$ + 2x × $\dfrac{1}{x}$ = 16

=> x² + $\dfrac{1}{ {x}^{2} }$ = 16 - 2

=> x² + $\dfrac{1}{ {x}^{2} }$ = 14

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We also have to find the value of x² - $\dfrac{1}{{x}^{2}}$

We have x = 2 - √3

Now .. squaring on both sides

=> x² = (2 - √3)²

=> (2)² + (√3)² - 2(2)(√3)

=> 4 + 3 - 4√3

=> 7 - 4√3

Also we have • $\dfrac{1}{x}\:=\: \dfrac{1}{2 \: - \: \sqrt{3} }$

Squaring on both sides ..

=> $\dfrac{1}{ {x}^{2} }$ = (2 + √3)²

=> (2)² + (√3)² + 4√3

=> 7 + 4√3

So..

• x² - $\dfrac{1}{ {x}^{2} }$ = 7 - 4√3 - (7 + 4√3)

=> 7 - 4√3 - 7 - 4√3

=> - 8√3

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x² + $\dfrac{1}{ {x}^{2} }$ = 14 and x² - $\dfrac{1}{ {x}^{2} }$ = - 8√3

________ [ ANSWER ]

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