Question

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?

Answer 1

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 or x + 5 = 0
x + 2 − 2 = 0 − 2 or x + 5 − 5 = 0 − 5
x = −2 or x = −5
Solutions = −2, −5

-5 is not a solution n the mistake is at this step: (Square root of x plus 6)^2 = (x + 4)^2

-5+6=1 and -5+4=-1 but after squaring, they become the same

Answer 2

He did not check for extraneous solutions.


Hoped this helped :D