Question

Find the solution of the square root of the quantity of x plus 2 plus 4 equals 6, and determine if it is an extraneous solution.

Answer 1

minus 4 both sides

square both sides

x+2=4
minus 2
x=2

the answer is
x = 2; not extraneous

Answer 2

Answer with Explanation:

`√(x+2+4)=6\\\\ √(x+6)=6`

Squaring Both sides

→x + 6 =36

→x +6 -6=36-6

→x=30

When we substitute , x=30 in the original equation ,we get

L H S

`=√(30 +6)\\\\=√(36)=\pm 6`

One value is 6 and other is ,-6.

So, x=30, is not an extraneous solution.

→→Secondly if your equation is

`√(x) +2+4=6\\\\ √(x)+6=6\\\\ √(x)=6-6\\\\ √(x)=0\\\\ x=0`

Substituting ,the value of x, in original equation

L H S

= 0 +2 +4

=6

=R HS

So, x=0, is also not an extraneous solution.

Or, if the equation is

`\rightarrow √(x+2) +4=6\\\\\rightarrow √(x+2)=6-4\\\\\rightarrow √(x+2)=2\\\\ \text{squaring both sides}\\\\ x +2=4\\\\ x=4-2\\\\x=2`

Substituting the value of ,x in original equation

LHS

`=√(2+2)+4\\\\= √(4)+4\\\\=2 +4=6`

=RHS

So, x=2 , is not an Extraneous Solution.