Question

If (x² - xy + y²) = 8 and (x⁴ + x²y² + y⁴) = 16, then find the value of (x² + xy + y²).

• A. 0
• B. 3
• C. 2
• D. 4

Answer 1

The Correct Option is C

Given, (x² + x²y² + y⁴) = 16
={(x² + y²)² - (xy)²} = 16
Since, a² - b² = (a - b)(a + b)
Therefore, (x² + y² + xy)(x² + y² - xy) = 16
Putting the value of (x² + y² - xy), we get
8(x² + y² + xy) = 16
Or, (x² + y² + xy) = \(\frac{16}{8}\) = 2
So, the correct option is (C) : 2.