2012/003) If 3a^2+2a-4=0 & 3b^2+2b-4=0 then, (1/a)+(1/b)=

a and b are root of equation

3x^2 + 2x - 4 = 0

so x^ 2+ (2/3) x - 4/3 = 0

sum of roots a + b = - 2/3
product of roots ab = - 4/3

so 1/a + 1/b = (b+a)/ab = (-2/3) / (-4/3) = 1/2

another method

a and b are root of equation

3x^2 + 2x - 4 = 0

so 1/a and 1/b are roots of equation

3(1/x)^2 + 2(1/x) - 4 = 0
or 4x^2-2x- 3 = 0

so 1/a + 1/b = 2/4 = 1/2(-coefficient of x/ coefficient of x^2)