Question

a^3 + b^3 =35 and a + b = 5 then a-b​

Answer 1

Given, a3 + b3 = 35

Using expansion,

(a + b) (a2 - ab + b2) = 35

⇒ (a + b) (a2 + b2 + 2ab -2ab – ab) = 35

⇒ (a + b) {(a + b)2 – 3ab} = 35

Since, ab = 6 (given)

⇒ (a + b) {(a + b)2 – 18} = 35

⇒ (a + b)3 – 18(a + b) – 35 = 0

Put a + b = x

⇒ x3 – 18x – 35 = 0

Using trial error method,

(Trick: Put values of x as given in the options)

Putting x = 5

L.H.S. = 125 – 90 – 35 = 0 = R.H.S.

∴ a + b = 5