Question

x^2+kx+7=0, x1-x2=1, k-?

Answer 1

x²+kx+7=0

x1+x2=-k
x1×x2=7


{x1+x2=-k
{x1-x2=1

x1+x2-x1-(-x2)=-k-1
x1+x2-x1+x2=-k-1
2x2=-k-1|÷2

x2=-(k+1)/2

x1+x2+x1-x2=-k+1
2x1=1-k|÷2

x1=(1-k)/2

x1×x2=7

((1-k)/2)×(-(k+1)/2)=7|×(-2)
(1-k)×(1+k)=-14
1-k²=-14
-k²=-14-1
-k²=-15|×(-1)
k²=15

k1=-√15
k2=√15