Question

resolva a equação ( x - 2x)(x-3a)+2a^2 = 3 (x^2 - 9a^2) +13a^2 ,sendo x a incógnita e U=R

Answer 1

(x-2x)(x-3a)+2a²=3(x²-9a²) +13a²
x²-3xa-2x²+6ax+2a²=3(x²-9a²)+13a²
-x²+3xa+2a²=3x²-27a²+13a²
-x²+3xa+2a²=3x²-14a²
3x²+x²-3xa-2a²-14a²=0
4x²-3ax-16a²=0

fazendo por bhaskara
-b±√b²-4ac/2a
-(-3a)±√(-3a)²-4(4)(-16a²)/2(4)
3a±√9a²+256a²/8
3a±√265a²/8

x'=3a+a√265/8
x"=3a-a√265/8

Answer 2

Olá!!

Resolução!!

( x-2x )( x-3a )+2a²=3( x²-9a² )+13a²
x²-3xa-2x²+6xa+2a²=3x²-27a²+13a²
x²-3xa-2x²+6xa+2a²-3x²+27a²-13a²=0
x²-3x²-2x²-3xa+6xa+27a²-13a²+2a²=0
- 4x² + 3xa + 16a² = 0 • ( - 1 )
4x² - 3xa - 16a²

a = 4, b = - 3a , c = - 16a²

∆ = b² - 4ac
∆ = ( - 3a )² - 4 • 4 • ( - 16a² )
∆ = 9a² + 256a²

x = - b ± √∆ / 2a
````````````````````````````__________
x = - ( - 3a ) ± √9a² + 256a² / 2 • 4

x = 3a ± √265a²/8

x = 3a ± a√265/8

x' = 3a + a√265/8

x" = 3a - a√265/8

S = { 3a - a√265/8, 3a + a√265/8 }

Espero ter ajudado!