If 4x² + y² = 40 and xy = 6, find the value of 2x + y and 2x - y.
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Correct answer: B
Explanation
Given:
4x² + y² = 40
xy = 6
By the formula:
(2x + y)² = 4x² + y² + 4xy
(2x − y)² = 4x² + y² − 4xy
(2x + y)² = 4x² + y² + 4xy
= 40 + 4(6)
= 40 + 24
= 64
2x + y = 8
(2x − y)²= 4x² + y² − 4xy
= 40 − 24
= 16
2x − y = 4
2x + y = 8, 2x − y = 4