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How do you solve #sqrt(x^2+5)=x+3#?

Answer 1

Kennedy Adams

Square both sides of the equation.

#(sqrt(x^2 + 5))^2 = (x + 3)^2#

#x^2 + 5 = x^2 + 6x + 9#

#x^2 - x^2 - 6x + 5 - 9 = 0#

#-6x = 4#

#x = -2/3#

Checking in the original equation, we find this solution works. Hence, the solution set is #{-2/3}#.

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Answer 2

Eva Adamson

To solve the equation sqrt(x^2+5)=x+3, we can follow these steps:

Square both sides of the equation to eliminate the square root: (sqrt(x^2+5))^2 = (x+3)^2.
Simplify the equation: x^2 + 5 = x^2 + 6x + 9.
Subtract x^2 from both sides to get rid of the x^2 terms: 5 = 6x + 9.
Subtract 9 from both sides: -4 = 6x.
Divide both sides by 6: x = -4/6, which simplifies to x = -2/3.

Therefore, the solution to the equation sqrt(x^2+5)=x+3 is x = -2/3.

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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.