If 3x + 2y = 13 and xy = 6, find the value of 9x^2 + 4y^2.
A85
B97
C109
D121
Explanation
Squaring both sides of (3x + 2y): (3x + 2y)^2 = 9x^2 + 12xy + 4y^2. 13^2 = 9x^2 + 12(6) + 4y^2 => 169 = 9x^2 + 72 + 4y^2 => 9x^2 + 4y^2 = 169 – 72 = 97.
Exam Relevance
- Topic: Algebra
- Subtopic: Identities
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