Question

(x^2-16x)^2-2(x^2-16x)-63=0
Urgent!

Answer 1

!!! este o ecuatie de gradul 4
 teoretic poate avea 4 (patru ) solutii reale

Fie x²-16x=u
 Ecuatia devine
u²-2u-63=0
  u²+7u-9u-63=0
 u(u+7)-9(u+7)=0
(u+7)(u-9)=0

u1=-7
 u2=9

x²-16x=-7
x²-16x+7=0
x=[16+-√(256-49)]/2
x1,2= (16+-√207)/2 , deci 2 solutii reale, Δ>0


x²-16x=9
x²-16x+9=0

x3,4=[16+-√(256-36)]/2
 x3,4=(16+-√220)/2= (16+-2√55)/2= 8+-√55,  alte 2 solutii reale, Δ>0

deci S= {(8-√55);(8+√55); (16-√207)/2; (16+√207)/2}