If x-2-3- then find the value of X2-1-X2

If x=2 √(3) x^2 1/x^2 = (x+1/x ) (x 1/x ) = (2 √(3)+1/2 √(3) ) (2 √(3) 1/2 √(3) ) = (4+3 4√(3)+1/2 √(3) ) (4+3 4√(3) 1/2 √(3) ) = (8 4√(3))(6 4√(3))/(2 √( ...

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Byju's Answer

Standard XII

Mathematics

Addition Rule of Differentiation

If x=2-√3, th...

Question

If x = 2 - $\sqrt{3}$ , then find the value of $X^{2} - \frac{1}{X^{2}}$

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Solution

If $x = 2 - \sqrt{3}$
$x^{2} - \frac{1}{x^{2}} = (x + \frac{1}{x}) (x - \frac{1}{x}) = (2 - \sqrt{3} + \frac{1}{2 - \sqrt{3}}) (2 - \sqrt{3} - \frac{1}{2 - \sqrt{3}}) = (\frac{4 + 3 - 4 \sqrt{3} + 1}{2 - \sqrt{3}}) (\frac{4 + 3 - 4 \sqrt{3} - 1}{2 - \sqrt{3}}) = \frac{(8 - 4 \sqrt{3}) (6 - 4 \sqrt{3})}{(2 - \sqrt{3})^{2}} = \frac{4 (/ 2 - \sqrt{3}) (6 - 4 \sqrt{3})}{(2 - \sqrt{3})} = \frac{8 (3 - 2 \sqrt{3})}{2 - \sqrt{3}} \times \frac{(2 + \sqrt{3})}{(2 + \sqrt{3})} = \frac{/ 48 + 24 \sqrt{3} - 32 \sqrt{3} - / 48}{4 - 3} = - 8 \sqrt{3}$

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If x = 2 - √3, then find the value of X2−1X2

If x=2−√3 x2−1x2=(x+1x)(x−1x)=(2−√3+12−√3)(2−√3−12−√3)=(4+3−4√3+12−√3)(4+3−4√3−12−√3)=(8−4√3)(6−4√3)(2−√3)2=4(/2−√3)(6−4√3)(2−√3)=8(3−2√3)2−√3×(2+√3)(2+√3)=/48+24√3−32√3−/484−3=−8√3

If x = 2 - $\sqrt{3}$ , then find the value of $X^{2} - \frac{1}{X^{2}}$