very very in maths Q

sqrt( x + 3sqrt(x + 1) ) = 3 ==>x + 3sqrt(x + 1) = 9
ok 不需要 check 因為 確定 3>0

x + 3sqrt(x + 1) = 9==>3sqrt(x + 1) = 9 - x
ok 移項不會產生問題

3sqrt(x + 1) = 9 - x==>9(x + 1) = 81 - 18x + x^2
平方可能產生重根需要check

9(x + 1) = 81 - 18x + x^2==>x^2 - 27x + 72 = 0
ok 移項不會產生問題

x^2 - 27x + 72 = 0==>(x - 3)(x - 24) = 0
ok 因式分解不會產生問題

(x - 3)(x - 24) = 0==>x = 3 or x = 24
ok

例
x=-3 ==>x^2=9 不能亂平方，為解題需要平方就要check

x^2-9=0
(x+3)(x-3)=0
so x=3 or x=-3

why do u need to check ?

since u changed the original equation to a quadratic equation and used the skill of quadratic equation to solve the problem.
hence, 3 and 24 are only the roots of x^2 - 27x + 72 = 0,
but not both of them can satisfy the original question {sqrt( x + 3sqrt(x + 1) ) = 3}. remember that the original question is not a quadratic equation.

so u need to check which one cant satisfy or if both of them can.
For those question with sqroot, fraction, log and so forth
u need to pay attention.


for thosesqroot questions, there cant be a negative number inside the sqroot
for those fraction questions, denominator cant equal zero
for those log problem, again there cant be a negative number inside log

當數字出現 x^1 和開方根號x 同時出現的時候