[tex] \left \{ {{ \sqrt{xy}=6} \atop {x^2+y^2=97}} \right. [/tex]. Created by ждлорп. algebra-ru

tex]...

ждлорп @ждлорп

July 2022 1 9 Report

[tex] \left \{ {{ \sqrt{xy}=6} \atop {x^2+y^2=97}} \right. [/tex]

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Verified answer

Xy >= 0
------------
V(xy) = 6 => xy = 36
-------------------------------
x^2 + y^2 + 2xy - 2xy = 97
(x+y)^2 - 2xy = 97
(x+y)^2 - 2*36 = 97
(x+y)^2 = 169
x+y = 13
y = 13-x
-------------
x*(13-x) = 36
x^2 - 13x + 36 = 0
x1 = 4
x2 = 9
y1 = 9
y2 = 4

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