if(x+y)=6 \: and \: xy=2 \: find \: the \: value \: of \: x3+y3
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Answered by
4
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.
Answered by
6
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
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