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Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain​

User Kiran Dash
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1 Answer

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√(x + 1) + 3 = 0 ==> √(x + 1) = -3

has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives

(√(x + 1))² = (-3)² ==> x + 1 = 9 ==> x = 8

But this is not a valid solution, since

√(8 + 1) = √9 = 3 ≠ -3

While -3 is a square root of 9, we had started off with the *positive* square root of x + 1.

User Kyohei Kaneko
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