If x4 + 2x3 + ax2 + bx + 9 is a perfect square, where a

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If x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the values of a and b are

1. a = 5, b = 6
2. a = 6, b = 7
3. a = 7, b = 6
4. a = 7, b = 8

Correct Option: C

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
∴ (x² + x + 3)² = x⁴ + x² + 9 + 2x³ + 6x + 6x²
= x⁴ + 2x³ + 7x² + 6x + 9
On comparing with x⁴ + 2x³ + ax² + bx + 9
a = 7, b = 6