Question

if ( 3x + 1 /2 ) (3x - 1/2 ) = 9x^2 - p​
plz give the answer​

Answer 1

$\Big(3x + \frac{1}{2} \Big)\Big(3x + \frac{1}{2} \Big) = 9x^{2} - p$

$\implies (3x)^{2} - \Big(\frac{1}{2}\Big)^{2} = 9x^{2} - p$

/* By Algebraic Identity */

$\boxed {\pink{ (a+b)(a-b) = a^{2} - b^{2} }}$

$\implies \cancel {9x^{2}} - \frac{1}{4}= \cancel {9x^{2}} - p$

$\implies - \frac{1}{4}= - p$

$\implies \frac{1}{4}= p$

Therefore.,

$\red { Value \: p } \green { = \frac{1}{4}}$

•••♪

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Equation :}}}$

$\:$

• $\footnotesize{\Big( 3x + \dfrac{1}{2}\Big)\Big(3x - \dfrac{1}{2} \Big) = {9x}^{2} - p}$

$\:$

$\bf{\underline{\underline{\bigstar\bigstar\: To \: Find :}}}$

$\:$

• Value of p

$\:$

$\bf{\underline{\underline{\bigstar\bigstar\:Formula \: use :}}}$

$\:$

• $\footnotesize{(a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:$

$\footnotesize{\Big( 3x + \dfrac{1}{2}\Big)\Big(3x - \dfrac{1}{2} \Big) = {9x}^{2} - p}$

$\footnotesize{\implies {\Big( 3x\Big)}^{2} {\Big( - \dfrac{1}{2} \Big)}^{2} = {9x}^{2} - p}$

$\footnotesize{\implies {9x}^{2} - \dfrac{1}{4} = {9x}^{2} - p}$

$\footnotesize{\implies {9x}^{2} - {9x}^{2} - \dfrac{1}{4} = - p}$

$\footnotesize{\implies - \dfrac{1}{4} = - p}$

$\footnotesize{\implies \dfrac{1}{4} = p}$

$\:$

$\bold{Value \: of \: p = \dfrac{1}{4}}$