Question

Solve for x: 9x² - 6px + (p² - q²) = 0​

Answer 1

Answer:

value of x = (p+q)/3 or (p-q)/3

Step-by-step explanation:

given that :

9x² - 6px + (p² - q²) = 0​

the above equation can be solved using

$x =$ [ $-(-6p)$ ± $\sqrt{(-6p)^2 - 4(9)(p^2-q^2)}$ ] ÷ 2(9)  ⇒ eq1

this is the most fundamental formula for solving x which is as

$x = -b$ ± $\sqrt{b^2-4ac}$   ÷ (2a)

where  $a = 9 ; b = (-6p) ; c = (p^2-q^2)$  from the general equation

$ax^2 + bx + c =0$

from eq 1 ;

x = [ 6p ± $\sqrt{36p^2-36p^2+36q^2}$ ] ÷ (18)

x  = [ 6p  ±  6q ] ÷ 18

x = [p  ±  q ] ÷ 3

x = (p+q)/3 or (p-q)/3

Answer 2

x is  (p - q)/3 or  (p + q)/3 for 9x² - 6px + (p² - q²) = 0​

Given:

• 9x² - 6px + (p² - q²) = 0​

To Find:

• Solve for x

Solution:

• a² - b² = (a + b)(a - b)

9x² - 6px + (p² - q²) = 0​

Step 1:

Rewrite -6p as -3p - 3p  and Add and subtract 3qx

9x² + (- 3p - 3p + 3q - 3q)x + (p² - q²) = 0​

Step 2:

Rearrange the term and rewrite (p² - q²)  as (p + q)(p -q)

9x²   - (3p - 3q)x    - (3p + 3q)x +(p + q)(p -q) = 0​

Step 3:

Take 3x common in 1st 2 terms and  -(p + q) common from last 2 terms

3x(3x    - (p - q))     - (p + q)(3x - (p -q))= 0​

Step 4:

Take (3x    - (p - q))  common

(3x    - (p - q)) (3x     - (p + q)) = 0​

Step 5:

Equate each factor with 0

3x    - (p - q) = 0 => x = (p - q)/3

3x     - (p + q) =0 => x = (p + q)/3

Hence x is (p - q)/3 or  (p + q)/3