Question

Encontre as raizes da equaçao ( x^2 - 3 )^2 + ( 2x^2 -1 )^2 = 88

Answer 1

Oi Eliy

(x² - 3)² + (2x² - 1)² = 88

x^4 - 6x² + 9 + 4x^4 - 4x² + 1 = 88

5x^4 - 10x² + 10 = 88

5x^4 - 10x² - 78 = 0

y = x²

5y² - 10y - 78 = 0

delta
d² = 100 + 4*5*78 = 1660
d = 2√415 

y1 = (10 + 2√415)/10 = (5 + √415)/5
y2 = (10 - 2√415)/10 = (5 - √415)/5 

x1 = √((5 + √415)/5) , x2 = -√((5 + √415)/5)