If x⁴ + x²y² + y⁴ = 29 and x² − xy + y² = 5, then what is the value of 5xy?
2020
If x⁴ + x²y² + y⁴ = 29 and x² − xy + y² = 5, then what is the value of 5xy?
- A.
0
- B.
2
- C.
-2
- D.
-1
Attempted by 35 students.
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Correct answer: B
First, factor the expression x⁴ + x²y² + y⁴ as (x² - xy + y²)(x² + xy + y²).
Substitute the given value 5 for (x² - xy + y²) to get 5(x² + xy + y²) = 29. Solve for x² + xy + y² to find it equals 5.8.
Subtract the original equation x² - xy + y² = 5 from this result to isolate 2xy. This gives 2xy = 0.8, so xy = 0.4.
Finally, multiply xy by 5 to find the value of 5xy is 2.