Posted by Jonathan on Sunday, May 20, 2012 at 10:29pm.
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
Remark :
( a - b ) ^ 2 = a ^ 2 - 2 * a * b + b ^ 2
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