Question

SOLVE WITH PROPER STEPS
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Answer 1

here is the attachment showing stepby step soln and mark as brainly

Answer 2

Answer:

x² + 1/x² = 14 and x² - 1/x² = -8√3

Step-by-step explanation:

Given that -

x = 2 - √3

$\frac{1}{x}=\frac{1}{2-\sqrt{3}} * \frac{2+\sqrt{3}}{2+\sqrt{3}}\\\\ \frac{1}{x}=\frac{2+\sqrt{3}}{(2)^2-(\sqrt{3})^2}\\\\ \frac{1}{x}=\frac{2+\sqrt{3}}{4-3}\\\\ \frac{1}{x}=\frac{2+\sqrt{3}}{1}\\\\ \frac{1}{x}=2+\sqrt{3}$

Now,

$x+\frac{1}{x}=2-\sqrt{3}+2+\sqrt{3}\\\\x+\frac{1}{x}=4$

Squaring both sides

$(x+\frac{1}{x})^2=(4)^2\\\\x^2+\frac{1}{x^2}+ 2*x*\frac{1}{x}= 16\\\\x^2+\frac{1}{x^2}+2=16\\\\x^2+\frac{1}{x^2}=16-2\\\\\boxed{\bf x^2+\frac{1}{x^2}=14}$

• To find x² - 1/x²

(2 - √3)² - (2 + √3)²

⇒ 4 + 3 - 4√3 - (4 + 3 + 4√3)

⇒ 7 - 4√3 - 7- 4√3

⇒ -8√3

Hence, x² + 1/x² = 14 and x² - 1/x² = -8√3