Решить систему уравнений[tex] {x}^{2} - {y}^{2} = - 32 \\ x + y = 16[/tex]. Created by ptyaev. algebra-ru

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ptyaev @ptyaev

August 2022 1 21 Report

Решить систему уравнений
[tex] {x}^{2} - {y}^{2} = - 32 \\ x + y = 16[/tex]

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Klick

Ответ: (7; 9)

Объяснение:

$\begin{cases}x^2-y^2=-32 \; (1)\\x+y=16 \; (2)\end{cases}\\(1)+2\cdot(2)\\x^2+2x-y^2+2y=0\\x^2+2x+1=y^2-2y+1\\(x+1)^2=(y-1)^2\\x_1=y_1-2 \Rightarrow y_1-2+y_1=16 \Rightarrow (x_1; y_1)=(7;9)\\x_2=-y_2\Rightarrow -y_2+y_2=16 \Rightarrow \varnothing$

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