f.4 mathz

if a and 1/a are the roots of the equation 2x^2+(k^2－1)x+(5－k)=0，find the values of
a) k =?
a and 1/a are the roots of the equation 2x^2+(k^2－1)x+(5－k)=0
=>1/a and a are the roots of the equation 2(1/x)^2+(k^2－1)(1/x)+(5－k)=0
2+(k^2－1)x+(5－k)x^2=0
(5－k)x^2+(k^2－1)x+2=0
So 2/(5－k)=(k^2－1)/(k^2－1)=(5－k)/2
k=3

b)a+1/a=?
2x^2+8x+2=0
x^2+4x+1= 0
a+1/a=－4

c)(a－1/a)^2=?
(a－1/a)^2
=(a+1/a)^2－4*a*1/a
=16－
=12

d)a^3+1/a^3=?
a^3+1/a^3
=(a+1/a)^3－3(a+1/a)
=(－4)^3－3*(－4)
=－64+12
=－52

a) Product of roots = a * 1/a = (5-k)/2

1 = (5-k)/2

k = 3