Question

if(x+y)=6 \: and \: xy=2 \: find \: the \: value \: of \: x3+y3​

Answer 1

Answer:

The value of x³ + y³ is 180.

Step-by-step-explanation:

We have given that,

x + y = 6

xy = 2

We have to find the value of x³ + y³.

Now, we know that,

( x + y )³ = x³ + y³ + 3x²y + 3xy²

x³ + y³ = ( x + y )³ - 3x²y - 3xy²

⇒ x³ + y³ = ( 6 )³ - 3xy ( x + y )

⇒ x³ + y³ = 216 - 3 * 2 * 6

⇒ x³ + y³ = 216 - 6 * 6

⇒ x³ + y³ = 216 - 36

⇒ x³ + y³ = 180

∴ The value of x³ + y³ is 180.

Answer 2

S O L U T I O N :

Here it is given that,

• x + y = 6
• xy = 2

As we know that formula of (x - y)³ = x³ + y³ + 3x²y + 3xy²

Now,

➝ x³ + y³ = (x + y)³ - 3xy (x + y)

➝ x³ + y³ = (6)³ - 3(2) × 6

➝ x³ + y³ = 216 - 6 × 6

➝ x³ + y³ = 216 - 36

➝ x³ + y³ = 180

∴ The value of x³ + y³ is 180