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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