Question

x= 1+ √ ̅x+5

x+5 is under one radical

the two answers are 4 and -1, but the teacher said -1 rejects; however, when i plug in the numbers, it works out. can someone explain why -1 rejects please?

Answer 1

-1 IS NOT equal to 1 + sqrt4

Answer 2

So -1 does not make the sentence true and must be rejected.

Answer 3

x = 1 + sqrt(x+5)
(x-1) = sqrt(x+5)
square both sides:
(x-1)^2 = x+5
x^2 - 2x + 1 - x - 5 = 0
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4 or x = -1

Try 4 in the original equation: x = 1 + sqrt(x+5)
LHS = 4
RHS = 1 + sqrt(4 + 5) = 1 + sqrt(9) = 1 + 3 = 4
LHS = RHS. x = 4 is a valid solution.

Try -1
LHS = -1
RHS = 1 + sqrt(-1+5) = 1 + sqrt(4) = 1 + 2 = 3

LHS is not equal to RHS. x = -1 is NOT a solution.

Answer 4

oh i kinda see. what does lhs and rhs stand for?

Answer 5

left hand side and right hand side

Answer 6

ohh so u have to see if x-1 = √x+5 ?

Answer 7

ok i understand now. thanks so much!!!!