Question

Se da ecuatia (m+1)x²-2(m-2)x+18=0 . Aflati m daca x1²+x2²=4 . Multumesc

Answer 1

x₁²+x₂²=4
(x₁+x₂)²-2 * x₁ * x₂=4

Folosim relatiile lui Viete: x₁+x₂ =- b/a
                                         x₁ * x₂= c/a
[ 2(m-2)/m+1 ]²- 2* 18/m+1 =4
4(m²-4m+4)/ (m+1)² - 36/m+1= 4
4m²-16m+16-36(m+1)/ (m+1)²= 4
4m²-16m+16-36m-36 =4(m+1)²
4m²-52m-20-4(m²+2m+1)=0
4m²-52m-20-4m²-8m-4=0
-60m-24=0
60m=-24
m= -24/60 = -2/5
S:m= -2/5