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

Answer: (C)

2

Answer 2

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.