Question

x-y = 7 x^3-y^3=1331 find xy and x^2 + y^2
please answer fast​

Answer 1

Answer:

1. xy = 47.04 (approx.)

2. x² + y² = 143.08 (approx.)

Step-by-step-explanation:

We have given that,

• x - y = 7

• x³ - y³ = 1331

We have to find,

• xy

• x² + y²

We know that,

( x - y )³ = x³ - 3x²y + 3xy² - y³ - - [ Identity ]

⇒ ( 7 )³ = x³ - y³ - 3x²y + 3xy²

⇒ 343 = 1331 - 3xy ( x - y )

⇒ 343 = 1331 - 3xy × 7

⇒ 343 = 1331 - 21xy

⇒ 21xy = 1331 - 343

⇒ 21xy = 988

⇒ xy = 988 / 21

⇒ xy = 47.047

⇒ xy = 47.04 - - ( 1 ) (approx.)

Now,

( x - y )² = x² - 2xy + y² - - [ Identity ]

⇒ ( 7 )² = x² + y² - 2 × 47.04 - - [ From ( 1 ) ]

⇒ 49 = x² + y² - 2 × 47.04

⇒ 49 = x² + y² - 94.08

⇒ 49 + 94.08 = x² + y²

⇒ x² + y² = 143.08 (approx.)

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Additional Information:

Some Algebraic Identities:

1. ( a + b )² = a² + 2ab + b²

2. ( a - b )² = a² - 2ab + b²

3. ( a + b )³ = a³ + 3a²b + 3ab² + b³

4. ( a - b )³ = a³ - 3a²b + 3ab² - b³

5. a² - b² = ( a + b ) ( a - b )

6. a² + b² = ( a + b )² - 2ab

7. a³ + b³ = ( a + b )³ - 3ab ( a + b )

8. a³ - b³ = ( a - b ) ( a² + ab + b² )