Question

if 9x square+48x+p is an perfect square , then the value of p is​

Answer 1

Answer:

p = 64

Step-by-step explanation:

 Given,  $9x^{2} + 48x + p$  is a perfect square.

Let  $9x^{2} + 48x + p = y^{2}$

$9(x^{2} + 48/9 x + p/9) = y^2}$

$x^{2} + 48/9 x + p/9 = (y/3)^{2}$

$x^{2} + 2(24/9)x + p/9 = (y/3)^{2}$

$x^{2} +2(24/9) + p/9 + (24/9)^{2} - (24/9)^{2} = (y/3)^{2}$

∴ $(p/9) = (24/9)^{2}$

$(p/9) = (576/81)$

∴ p = 64.

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Answer 2

Step-by-step explanation:

Given, 9x²+48x+p is a perfect square.

Let 9x² + 48x + p = y²

9(x^{2} + 48/9 x + p/9) = y^2}

x² +48/9x+p/9 = (y/3)2

x² + 2(24/9)x+p/9 = (y/3)²

x² + 2(24/9) +p/9 + (24/9)² −

(24/9)2 = (y/3)2

(p/9) = (24/9)2

(p/9) (576/81)

: p = 64.