Question

SOLVE : (X + 2) (X + 3) + (X - 2) (X - 3) - 2X(X+1) = 0

Answer 1

Step-by-step explanation:

Given that,

(x+2)(x+3)+(x−3)(x−2)−2x(x+1)=0⇒x+2x+3x+6+x 2

−3x−2x+6−2x

2

−2x=0

⇒2x

2

−2x

2

+5x−5x−2x+12=0

⇒−2x+12=0

⇒−2x=−12

⇒x=6

Answer 2

Answer:

Given:-

Solve : ( x + 2 ) ( x + 3 ) + ( x - 2 ) ( x - 3 ) - 2x ( x + 1 ) = 0.

To Find:-

The value of "x".

Note:-

●》Here, we will first open brackets by direct method and then add/subtract common term. At last, we will transpose the terms to find the value of "x".

●》Transposing - It is a process in which we change the side of known value for finding unknown value and in this process signs are also changed. For example - Positive becomes Negative, Multiple becomes Divisional.

Solution:-

$\huge\red{( x + 2 ) ( x + 3 ) + ( x - 2 ) ( x - 3 ) - 2x ( x + 1 ) = 0}$

$\huge\red{ \ \ \ \ The \ \ value \ \ of \ \ x = ?}$

☆ According to note first point, using direct method to open brackets~

▪︎$( x + 2 ) ( x + 3 ) + ( x - 2 ) ( x - 3 ) - 2x ( x + 1 ) = 0$

▪︎$( x × x ) + ( x × 3 + 2 × x ) + ( 2 × 3 ) + ( x × x ) + ( x × -3 + -2 × x ) + ( -2 × -3 ) - ( 2x × x + 2x × 1 ) = 0$

☆ As positive sign × negative sign = negative sign, negative sign × negative sign = positive sign, negative sign × positive sign = negative sign~

▪︎$x² + ( 3x + 2x ) + ( 6 ) + x² + ( -3x - 2x ) + ( 6 ) - ( 2x² + 2x ) = 0$

▪︎$x² + ( 5x ) + ( 6 ) + x² + ( -5x ) + ( 6 ) - ( 2x² + 2x ) = 0$

☆ Multiplying the outer sign into brackets sign to remove brackets~

▪︎$x² + 5x + 6 + x² - 5x + 6 - 2x² - 2x = 0$

☆ Taking common terms one side~

▪︎$x² + x² - 2x² + 5x - 5x - 2x + 6 + 6 = 0$

▪︎$2x² - 2x² - 2x + 12 = 0$

▪︎$-2x + 12 = 0$

☆ According to note second point ( Transposing )~

▪︎$-2x = 0 - 12$

▪︎$-2 × x = -12$

▪︎$x = \dfrac{-12}{-2}$

☆ After dividing, negative signs will be canceled~

▪︎$x = 6$

$\huge\pink{The \ \ value \ \ of \ \ x = 6}$

Checking:-

♤ Let's check for "x" as per equation means ( L.H.S = R.H.S )~

• $( x + 2 ) ( x + 3 ) + ( x - 2 ) ( x - 3 ) - 2x ( x + 1 ) = 0 \implies ?$

♤ Applying "x" value~

• $( 6 + 2 ) ( 6 + 3 ) + ( 6 - 2 ) ( 6 - 3 ) - 2 × 6 ( 6 + 1 ) = 0 \implies ?$

• $( 8 ) ( 9 ) + ( 4 ) ( 3 ) - 12 ( 7 ) = 0 \implies ?$

• $8 × 9 + 4 × 3 - 12 × 7 = 0 \implies ?$

• $72 + 12 - 84 = 0 \implies ?$

• $84 - 84 = 0 \implies ?$

• $0 = 0 \implies ✔$

$\huge\green{Hence, Proved : x = 6}$

Answer:-

Hence, the value of "x" = 6.

:)