Question

Решите уравнение.
а)
$4 {x}^{2} - 36 = 0$
б)
$\frac{x}{x - 2} + \frac{6}{x + 2} = \frac{21}{ {x}^{2} - 4}$
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Answer 1

4х²-36=0 ;

4х²=36 |:4 ;

х²=9 ;→х=±√9 ;

х=±3 ;

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х/(х-2)+6/(х+2)=21/(х²-4) ;

х/(х-2)+6/(х+2)-21/(х²-2²)=0 ;

х/(х-2)+6/(х+2)-21/((х-2)(х+2))=0 ;

(х(х+2)+6(х-2)-21)/((х-2)(х+2))=0 ;

(х²+2х+6х-12-21)/((х-2)(х+2))=0 ;

(х²+8х-33)/((х-2)(х+2))=0 ;

х²+8х-33=0 ;

D=8²-4*1*(-33)=64+132=196=14² ;

x₁=(-8-14)/2=-22/2=-11 ;

x₂=(-8+14)/2=6/2=3.