Question

sa se rezolve ecuatia x^2+px+35=0 stiind ca suma patratelor solutiilor ecuatiei este egala cu 74

Answer 1

x²+px+35=0
relatiile lui Viete
a=1
b=p
c=35
x₁+x₂=-b/a=p/1=p
x₁ × x₂=c/a=35/1=35
x₁²+x₂²=74
x₁²+x₂²+2x₁×x₂=74+2×35
(x₁+x₂)² =144
p²=144
p=√144=+/-12

p=12
x²+12x+35=0
x²+7x+5x+35=0
x(x+7)+5(x+7)=0
(x+7)(x+5)=0
x=-7
x=-5

p=-12
x²-12x+35=0
x²-7x-5x+35=0
x(x-7)-5(x-7)=0
(x-7)(x-5)=0
x=7
x=5