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$x+y=8$, $x-y=6$ হলে, $x^2+y^2$ এর মান কত?

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$x+y=8$, $x-y=6$ হলে, $x^2+y^2$ এর মান কত?

Options :

  • (A) $40$
  • (B) $60$
  • (C) $50$
  • (D) $80$

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আমরা জানি,
$2\left(x^2+y^2\right)=\left(x+y\right)^2+\left(x-y\right)^2$

বা, $2\left(x^2+y^2\right) = 8^2+6^2$

বা, $2\left(x^2+y^2\right) = 64+36$

বা, $2\left(x^2+y^2\right) = 100$

বা, $\left(x^2+y^2\right) = \frac{100}{2}$

$\therefore x^2+y^2 = 50$

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