Question

Please help!!!!
(square root of x) + 3 = square root of (x+12)

Answer 1

sqrt ( x ) + 3 = sqrt ( x + 12 ) Subtract 3 from both sides:

sqrt ( x ) + 3 - 3 = sqrt ( x + 12 ) - 3

sqrt ( x ) = sqrt ( x + 12 ) - 3

Square both sides :

[ sqrt ( x ) ] ^ 2 = [ sqrt ( x + 12 ) ] ^ 2
- 2 * sqrt ( x + 12 ) * 3 + 3 ^ 2

x = x + 12 - 6 sqrt ( x + 12 ) + 9

x = x - 6 sqrt ( x + 12 ) + 21

Add 6 sqrt ( x + 12 ) from both sides:

x + 6 sqrt ( x + 12 ) = x - 6 sqrt ( x + 12 ) + 21 + 6 sqrt ( x + 12 )

x + 6 sqrt ( x + 12 ) = x + 21 Subtract x from both sides:

x + 6 sqrt ( x + 12 ) - x = x + 21 - x

6 sqrt ( x + 12 ) = 21 Square both sides

6 ^ 2 * [ sqrt ( x + 12 ) ] ^ 2 = 21 ^ 2

36 ( x + 12 ) = 441

36 x + 36 * 12 = 441

36 x + 432 = 441 Subtract 432 from both sides

36 x + 432 - 432 = 441 - 432

36 x = 9 Divide both sides by 36

x = 9 / 36 = 9 / ( 9 * 4 ) = 1 / 4


x = 1 / 4

Answer 2

Remark :

( a - b ) ^ 2 = a ^ 2 - 2 * a * b + b ^ 2