যদি $x (4 - \sqrt{3}) = y (4 + \sqrt{3}) = 1$ হয়, তাহলে $x^{2} + y^{2}$ -এর মান হবে _____

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Moumita De36 February 24, 2025 0 Comments

score 0 · Answer 1 · 2025-02-24T06:37:05+00:00

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$x (4 - \sqrt{3}) = y (4 + \sqrt{3}) = 1$

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

$y = \frac{1}{4 + \sqrt{3}}$

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

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

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

$x^{2} + y^{2} = \frac{38}{169}$

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