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How do you solve #sqrt(x+3)= x-3#?

Answer 1

Ethan Adkins

#x=+1" and "x=+6#

Square both sides

#x+3=(x-3)^2" "->" "x+3=x^2-6x+9#

Subtract #x# from both sides

#3=x^2-7x+9#

Subtract 3 from both sides

#0=x^2-7x+6#

Notice that #(-1)xx(-6) = +6" and "-1-6=-7#

Factorising

#=>0=(x-1)(x-6)#

#x=+1" and "x=+6#

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Answer 2

Avery Alexander

To solve the equation sqrt(x+3) = x-3, we can follow these steps:

Square both sides of the equation to eliminate the square root: (sqrt(x+3))^2 = (x-3)^2.
Simplify the equation: x+3 = (x-3)^2.
Expand the right side of the equation: x+3 = x^2 - 6x + 9.
Rearrange the equation to form a quadratic equation: x^2 - 7x + 6 = 0.
Factor the quadratic equation: (x-6)(x-1) = 0.
Set each factor equal to zero and solve for x: x-6 = 0 or x-1 = 0.
Solve for x in each equation: x = 6 or x = 1.

Therefore, the solutions to the equation sqrt(x+3) = x-3 are x = 6 and x = 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.