Question

Dentify all of the following solutions of square root of x plus 10 end root minus 4 equals x

Answers

x = −6

x = −1

x = −6 and x = −1

None of the above

Answer 1

x=-1

Explanation:

sqrt(x+10) -4= x

sqrt(x+10) = x+4

square each side

x+10=(x+4)^2

x+10= x^2+8x+16

subtract x+10 from each side

x^2+7x+6=0

(x+6)(x+1)=0

x=-6 x=-1

Then we plug both back into the equation.

sqrt(-1+10) -4= -1

sqrt(9) -4= -1

3-4 = -1

-1=-1. this works out.

sqrt(-6+10) -4 = -6

sqrt(4) -4= -6

2-4= -6

-2= -6. this does not work so the only solution is x=-1

Answer 2

x = -1.

Explanation:

√(x + 10) - 4 = x

√(x + 10) = x + 4

Squaring both sides:

x + 10 = x^2 + 8x + 16

x^2 + 8x - x + 6 = 0

x^2 + 7x + 6 = 0

(x + 6)(x + 1) = 0

x = -6, -1.

Check for any extraneous roots:

√(x + 10) - 4 = x

Try x = -6:

√(-6 + 10) - 4 = 2 - 4 = -2.

but we found x = -6 , so -6 is not a root.

Try x = -1:

√(-1 + 10) - 4 = 3 - 4 = -1. So x = -1 is a root.