Question

Sa se rezolve ecuatia:
(x2 - 16x)totul la patrat - 2 (x2 -16x)-63 =0 unde x2 este x la patrat

Answer 1

(x²-16x)² - 2 (x² -16x)-63 =0

(x²-16x)=a
a²-2a-63=0
a²-9a+7a-63=0
a(a-9)+7(a-9)=0
(a-9)(a+7)=0
a=9
a=-7


x²-16x=9
x²-16x-9=0
Δ=16²+36=256+36=292
x₁ =(16+√292)/2=(16+2√73)/2=8+√73
x₂ =(16-√292)/2=(16-2√73)/2=8-√73

x²-16x=-7
x²-16x+7=0
Δ=16²-28=256-28=228
x₁ =(16+√228)/2=(16+2√57)/2=8+√57
x₂ =(16-√228)/2=(16-2√57)/2=8-√57