Question

It, x^3+ y^3=
18 and
xy=1
so prove this, (x+y) =3​

Answer 1

Answer:

Prove (x + y) = 3 is given below

Step-by-step explanation:

   x³+y³ = 18   and xy = 1

⇒(x + y) (x² - xy + y²) = 18

⇒ (x + y) {(x + y)² -3xy} = 18

⇒ (x + y) {(x + y)² -3} = 18

⇒ (x+ y)³ - 3 (x +y) - 18 = 0

⇒ P³ -3P - 18 = 0     [Let P = (x +y)]

⇒ P³ - 3P² + 3P² -9P + 6P - 18 = 0

⇒ P²(P - 3) +3P(P - 3) +6(P - 3) = 0

⇒ (P - 3) (P² + 3P +6) = 0

∴ (P - 3) = 0

⇒ (x + y) - 3 = 0

⇒ (x + y) = 3 [Proved]