Найдите x из пропорции: [tex]\frac{9 - 4a^{2} - 4ab - b^{2}}{4a^{2} + 2ab + 3b - 9} = \frac{3 + 2a + b}{x}[/tex]. Created by andromeda12. algebra-ru

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andromeda12 @andromeda12

July 2022 1 10 Report

Найдите x из пропорции:
[tex]\frac{9 - 4a^{2} - 4ab - b^{2}}{4a^{2} + 2ab + 3b - 9} = \frac{3 + 2a + b}{x}[/tex]

Answers & Comments

skvrttt

$\frac{9-4a^2-4ab-b^2}{4a^2+2ab+3b-9}=\frac{3+2a+b}{x}$ , следовательно,

$\displaystyle x=\frac{(3+2a+b)(4a^2-9+2ab+3b)}{9-(4a^2+4ab+b^2)}=\frac{(3+2a+b)((2a-3)(2a+3)+(2a+3)b)}{9-(2a+b)^2}=\\\frac{(3+2a+b)(2a+3)(2a-3+b)}{(3-2a-b)(3+2a+b)}=-2a-3}$

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