If x4 + x2y2 + y4 = 63, and x2 + xy + y2 = 7, then find the value

1.	If x4 + x2y2 + y4 = 63, and x2 + xy + y2 = 7, then find the value of (x/y + y/x) ?1. -42. 83. -84. 4
Answer» Correct Answer - Option 3 : -8 Calculation: As we know that, x4 + x2y2 + y4 = (x² - xy +y²) (x² + xy + y²) According to the question x⁴ + x2y2 + y4 = 63, and x2 + xy + y2 = 7 . . . (1) ⇒ 63 = (x2 - xy +y2) × 7 ⇒ (x2 - xy +y2) = 9 . . . (2) Add equation (1) and (2) ⇒ 2(x² + y²) = 16 ⇒ x² + y² = 8 The value of (x² + y²) put in equation (1) ⇒ xy = 7 - 8 = -1 Now, ⇒ (x/y + y/x) ⇒ (x² + y²)/xy ⇒ 8/-1 ⇒ -8 ∴ The required value is -8.

If x4 + x2y2 + y4 = 63, and x2 + xy + y2 = 7, then find the value of (x/y + y/x) ?1. -42. 83. -84. 4

Answer» Correct Answer - Option 3 : -8

Calculation:

As we know that,

x4 + x2y2 + y4 = (x² - xy +y²) (x² + xy + y²)

According to the question

x⁴ + x2y2 + y4 = 63, and

x2 + xy + y2 = 7 . . . (1)

⇒ 63 = (x2 - xy +y2) × 7

⇒ (x2 - xy +y2) = 9 . . . (2)

Add equation (1) and (2)

⇒ 2(x² + y²) = 16

⇒ x² + y² = 8

The value of (x² + y²) put in equation (1)

⇒ xy = 7 - 8 = -1

Now,

⇒ (x/y + y/x)

⇒ (x² + y²)/xy

⇒ 8/-1

⇒ -8

∴ The required value is -8.

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If x4 + x2y2 + y4 = 63, and x2 + xy + y2 = 7, then find the value of (x/y + y/x) ?1. -42. 83. -84. 4

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