Question

If 9x²+Px+25 is a perfect square, then find the value of P​

Answer 1

30 is the value of P
Steps:
A perfect square follows the pattern $a^2+2ab+b^2\\\boxed{a=3,b=5}\\\boxed{2ab=30}$

Answer 2

Answer:

P = 30

Step-by-step explanation:

A perfect square of the form

(ax + b)² = a²x² + 2abx + b²

9x² = (3x)² ⇒ a = 3 and 25 = 5² ⇒ b = 5

2abx = 2 × 3 × 5x = 30x

9x² + 30x + 25 = (3x + 5)² ← a perfect square

P = 2ab = 30