Question

if a and b are the roots of the equation x^2+2x+4=0 then 1/a^3+1b^3

Answer 1

I hope this answer help you

Answer 2

HELLO DEAR,

given that:-

x² + 2x + 4 = 0

a = 1 , b = 2 , c = 4

and , "A" & "B" are the roots of the equation

Now,

we know that:-

sum of roots = -b/a

⇒ A + B = -b/a = -2/1 = (-2)

⇒(A + B)³ = (-2)³ = (-8)

product of roots = c/a

A * B = c/a = 4/1 = 4

⇒(A * B) = (4)³ = 64

Now,

1/A³ + 1/B³ = (B³ + A³)/(A*B)³

⇒ [ (A + B)³ - 3AB(A + B) ] / (A * B)³
∴ [ (x + y)³ = x³ + y³ + 3ab(a + b) , (x³ + y³) = (x + y)³ - 3ab(a + b) ]

⇒[ (-8) - 3*4(-2) ] /(64)

⇒ [ -8 + 24 ] / 64

⇒16/64

⇒1/4

I HOPE ITS HELP YOU DEAR,
THANKS