Question

If x² + y² = 221 and x - y = I then the value of x³ - y³ is​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

The value of x³ - y³ is 331.

Step-by-step-explanation:

We have given that,

x² + y² = 221 - - - ( 1 ) &

x - y = 1 - - - ( 2 )

We have to find the value of x³ - y³.

Now,

x - y = 1 - - - ( 2 )

⇒ x = 1 + y

⇒ x = y + 1 - - - ( 3 )

By substituting this value in equation ( 1 ), we get,

x² + y² = 221 - - - ( 1 )

⇒ ( y + 1 )² + y² = 221

⇒ y² + 2y + 1 + y² = 221

⇒ y² + y² + 2y + 1 - 221 = 0

⇒ 2y² + 2y - 220 = 0

⇒ y² + y - 110 = 0

⇒ y² + 11y - 10y - 110 = 0

⇒ y ( y + 11 ) - 10 ( y + 11 ) = 0

⇒ ( y + 11 ) ( y - 10 ) = 0

⇒ ( y + 11 ) = 0 OR ( y - 10 ) = 0

⇒ y + 11 = 0 OR y - 10 = 0

⇒ y = - 11 OR y = 10

Now, by substituting y = - 11 in equation ( 3 ), we get,

x = y + 1 - - - ( 3 )

⇒ x = - 11 + 1

⇒ x = - 10

Now,

x³ - y³ = ( - 10 )³ - ( - 11 )³

⇒ x³ - y³ = - 1000 - ( - 1331 )

⇒ x³ - y³ = - 1000 + 1331

⇒ x³ - y³ = 331

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Now, by substituting y = 10 in equation ( 3 ), we get,

x = y + 1 - - - ( 3 )

⇒ x = 10 + 1

⇒ x = 11

Now,

x³ - y³ = ( 11 )³ - ( 10 )³

⇒ x³ - y³ = 1331 - 1000

⇒ x³ - y³ = 331

∴ The value of x³ - y³ is 331.