Israel started to solve a radical equation in this way
Square root of x plus 6 − 4 = x
Square root of x plus 6 − 4 + 4 = x + 4
Square root of x plus 6 = x + 4
( Square root of x plus 6 )2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 - 6 = x2 + 8x + 16 - 6
x = x2 + 8x + 10
x - x = x2 + 8x + 10 - x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)

x + 2 = 0 x + 5 = 0
x + 2 - 2 = 0 - 2 x + 5 - 5 = 0 - 5
x = -2 x = -5

Solutions = -2, -5

What error did Israel make? (2 points)

He subtracted 6 before subtracting x.

He added 4 before squaring both sides.

He factored x2 + 7x + 10 incorrectly.

He did not check for extraneous solutions.

Question

contestada

Respuesta :

AlonsoDehner AlonsoDehner · Answer 1 · 2019-02-26T00:51:58+01:00

Answer:

Option 4 is correct.

He did not check for extraneous solutions.

Step-by-step explanation:

THe given equation is

[tex]\sqrt{x+6} -4=x[/tex]

Hence it is implied here that on left side only positive root is considered

While solving the student squared and got two answers.

He has to substitute and check whether valid only for positive square root.

Substitute x=-2

Left side =2-4 =-2 and right side = -2 which are equal

Hence x=-2 can be a solution

Next is x=-5

Left side = 1-4 = -3 and right side =-5

Both are not equal

Thus only solution is x =-2

Option 4 is correct