Question

. If (x+3)² = (x-3)², what is the value of x?

Answer 1

Given :

(x+3)² = (x-3)²

To Find :

Value of x

Formula used :

$\sf\:(x+y)^2=x^2+y^2+2xy$

$\sf\:(x-y)^2=x^2+y^2-2xy$

Solution :

We have

$\sf\:(x+3)^2=(x-3)^3$

$\sf\implies\:x^2+9+2\times3\times\:(x)=x^2+9-2\times3\times\:(x)$

$\sf\implies\:x^2+9+6x=x^2+9-6x$

$\sf\implies\:x^2+9+6x-x^2-9+6x=0$

$\sf\implies\:12x=0$

$\sf\implies\:x=0$

Therefore, the value of x = 0

Answer 2

$\rule{200}3$

$\huge\tt{GIVEN:}$

• (x+3)² = (x-3)²

$\rule{200}3$

$\huge\tt{TO~FIND:}$

• The value of x

$\rule{200}3$

$\huge\tt{FORMULA~USED:}$

• (x+y)²=x²+y²+2xy
• (x-y)²=x²+y²-2xy

$\rule{200}3$

$\huge\tt{SOLUTION:}$

➠ ( x + 3 )² = ( x - 3 )³

➠ x² + 9 + 2 × 3 × (x) = x² + 9

➠x² + 9 + 6x = x² + 9 - 6x

➠x² + 9 + 6x - x² - 9 + 6x = 0

➠x² - x² + 6x + 9 - 9 = 0

➠6x + x² - x² = 0

➠x = 0

$\rule{200}3$