If x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0, then what is the valu

1.	If x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0, then what is the value of x3 + 8y3?1. 852. 653. 764. 95
Answer» Correct Answer - Option 2 : 65 Given - x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0 Formula used - a³ + b³ = (a + b) (a² - ab + b²) (a + b)² = a² + b² + 2ab Solution - x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0 ⇒ xy = 2 then, 4xy = 8 ⇒ (x + 2y)² = x² + 4y² + 4xy = 17 + 8 = 25 ⇒ (x + 2y) = 5 ⇒ x3 + 8y³ = (x + 2y) (x² + 4y² - 2xy) ⇒ x3 + 8y³ = (5) × (17 - 4) = 65 ∴ x3 + 8y³ = 65. Short trick - ⇒ put x = 1, y = 2 ⇒ it satisfy both the given expression. ⇒x3 + 8y³ = 1³ + 8 × 2³ = 65

If x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0, then what is the value of x3 + 8y3?1. 852. 653. 764. 95

Answer» Correct Answer - Option 2 : 65

Given -

x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0

Formula used -

a³ + b³ = (a + b) (a² - ab + b²)

(a + b)² = a² + b² + 2ab

Solution -

x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0

⇒ xy = 2 then, 4xy = 8

⇒ (x + 2y)² = x² + 4y² + 4xy = 17 + 8 = 25

⇒ (x + 2y) = 5

⇒ x3 + 8y³ = (x + 2y) (x² + 4y² - 2xy)

⇒ x3 + 8y³ = (5) × (17 - 4) = 65

∴ x3 + 8y³ = 65.

Short trick -

⇒ put x = 1, y = 2

⇒ it satisfy both the given expression.

⇒x3 + 8y³ = 1³ + 8 × 2³ = 65

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If x2 + 4y2 = 17 and xy = 2, where x > 0, y > 0, then what is the value of x3 + 8y3?1. 852. 653. 764. 95

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