If x⁴ + x²y² + y⁴ = 37 and x² - xy + y² = 5, then what is the value of xy?
2020
If x⁴ + x²y² + y⁴ = 37 and x² - xy + y² = 5, then what is the value of xy?
- A.
0
- B.
-1
- C.
1.2
- D.
-1.2
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Use (x² - xy + y²)(x² + xy + y²) = x⁴ + x²y² + y⁴.
Given x² - xy + y² = 5 and x⁴ + x²y² + y⁴ = 37.
So x² + xy + y² = 37/5 = 7.4.
Subtracting the two equations gives 2xy = 7.4 - 5 = 2.4, hence xy = 1.2.