Question

If alpha and beta are the zeroes of x²- px+q, then find tha value of alpha cube plus beta cube

Answer 1

◀ HEY THERE!!◀

 ◀  Question:

→   If alpha and beta are the zeroes of x²- px+q, then find tha value of alpha³ + beta³ ?

 ◀ Method of Solution:

 →Sum of Zeroes = -b/a => -(Coefficient of x)/ Coefficient of x²

→ Product of Zeroes = c/a => (Constant term)/Coefficient of x²

Here,  ⇒ Sum of Zeroes = -(-p)/ a => p

⇒   Product of Zeroes = q/ 1 => q

◀   Now, According to the Question's Statement!◀

→  Find the Value of a³+b³=?

◀ Formula of a³+b³ = (a+b)(a²-ab+b²)◀

→ We have, (a+b) = p , (ab) = q

⇒  a³+b³ = (a+b) [(a+b)²-2ab-ab]

 ⇒  (p)[(p)² -3q)]

⇒  p[p²-3q]

 ⇒ p³-3pq

Hence, → Value of a³+b³ = p³-3pq ◀

Answer 2

Find the Value of a³+b³=?


Formula of a³+b³ = (a+b)(a²-ab+b²)

We have

(a+b) = p

(ab) = q

a³+b³ = (a+b) [(a+b)²-2ab-ab]

(p)(p)² -3q)

p(p²-3q)

p³-3pq


Therefore, Value of a³+b³ = p³-3pq