Question

Cum se rezolva exercițiile de tipul???

$x { + y} = 21$
$x {}^{2} + y {}^{2} = 223$

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Answer 1

x+y = 21

x²+y² = 223 ⇒ (x+y)²-2xy = 223

⇒ 21²-2xy = 223 = 441-2xy = 223

⇒ 2xy = 218 ⇒ xy = 109

x+y = 21

xy = 109

t² - St + P = 0

t² - 21t + 109 = 0

∆ = 21² - 4•109 = 441 - 436 = 5

⇒ t₁,₂ = (21±√5)/2

$\Rightarrow (a,b) = \left\{\left(\dfrac{21-\sqrt 5}{2},\dfrac{21+\sqrt 5}{2}\right);\left(\dfrac{21+\sqrt 5}{2},\dfrac{21-\sqrt 5}{2}\right)\right\}$