solve radical equation sqrt x+6=x

Question

radical equations

Answer 1

sqrt (x+6) = x

Squaring on each side.

x+6 = x^2

Subtract x,6 from each side.

x+6-x-6 = x^2-x-6

x^2-x-6 = 0

x^2-3x+2x-6 = 0

x(x-3)+2(x-3) = 0

(x-3)+(x+2) = 0

(x-3) = 0                     and     (x+2) = 0

Add 3 to each side.            Subtract 2 from each side.

x-3+3 = 0+3                          x+2-2 = 0-2

x = 3                                      x = -2

Solution of given radical equation is x = 3,-2.

Comments

x = 3     and        x = - 2.

Check :

• Substitute the value x = 3 in original equation.

√(3 + 6) = 3

√9 = 3

3 = 3.

The above satatement is true.

So, x = 3 is a solution of √(x + 6) = x.

• Substitute the value x = - 2 in original equation.

√(- 2 + 6) = - 2

√4 = - 2

2 = - 2.

The above satatement is false.

So, x = - 2 is not a solution of √(x + 6) = x.

Finally, solution of √(x + 6) = x is x = 3.