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VerifySolutions—Wolfram Documentation

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VerifySolutions

is an option to Solve and related functions that controls whether to verify solutions.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
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VerifySolutions

VerifySolutions

is an option to Solve and related functions that controls whether to verify solutions.

Details

  • VerifySolutions controls whether the solutions obtained using non-equivalent transformations or numerical methods should be verified.
  • Possible settings include:
  • Automaticautomatically determine whether to verify
    Trueattempt to verify
    Falsedo not verify

Examples

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Basic Examples  (1)

Solve an equation:

Wolfram Language code: Solve[Sqrt[x] + x == -2, x, VerifySolutions -> False]

Use VerifySolutions to check if they are solutions or not:

Wolfram Language code: Solve[Sqrt[x] + x == -2, x, VerifySolutions -> True]
Wolfram Language code: x^1 / 2 + x == -2 /. x -> (1/2)(-3 - ISqrt[7])

Scope  (4)

Solve verifies solutions obtained using non-equivalent transformations:

Wolfram Language code: eqns = Sqrt[x + Sqrt[x]] == 2 && y ^ 9 - y - 2x ^ (1 / 7) == 3;
Wolfram Language code: sol1 = Solve[eqns, {x, y}];//Timing

With VerifySolutions False, Solve does not verify the solutions:

Wolfram Language code: sol2 = Solve[eqns, {x, y}, VerifySolutions -> False];//Timing

Some of the solutions returned with VerifySolutions False are not correct:

Wolfram Language code: Length /@ {sol1, sol2}

Use a fast numeric test in an attempt to select correct solutions:

Wolfram Language code: sol3 = Select[sol2, TrueQ[eqns /. N[#, 20]]&];//Timing

In this case, numeric verification gives the correct solution set:

Wolfram Language code: sol3 === sol1

Reduce returns only the correct solutions:

Wolfram Language code: Reduce[eqns, {x, y}]
Wolfram Language code: Length[%]

Solve an equation symbolically without verifying the solution:

Wolfram Language code: solns = Solve[Sqrt[x] + x == -2, x, VerifySolutions -> False]

This can yield solutions that are not mathematically valid:

Wolfram Language code: Table[Sqrt[x] + x == -2 /. soln, {soln, solns}]

Solve the same equation numerically:

Wolfram Language code: nsolns = NSolve[Sqrt[x] + x == -2, x, VerifySolutions -> False]

Note the unverified solutions do not satisfy the given equation:

Wolfram Language code: Table[Sqrt[x] + x == -2 /. soln, {soln, nsolns}]

Verifying the solution discards the invalid result, returning an empty list indicating there are no solutions:

Wolfram Language code: Solve[Sqrt[x] + x == -2, x, VerifySolutions -> True]
Wolfram Language code: NSolve[Sqrt[x] + x == -2, x, VerifySolutions -> True]

Using Automatic solution verification attempts to detect and discard possibly invalid results:

Wolfram Language code: Solve[Sqrt[x] + x == -2, x, VerifySolutions -> Automatic]
Wolfram Language code: NSolve[Sqrt[x] + x == -2, x, VerifySolutions -> Automatic]

Properties & Relations  (1)

Using Solve without solution verification can give mathematically incorrect results:

Wolfram Language code: solns = Solve[Sqrt[x] + x == -4, x, VerifySolutions -> False]

Using Reduce will return False if no solutions exist:

Wolfram Language code: With[{a = -2}, Reduce[Sqrt[x] + x == a, x]]
Wolfram Research (1988), VerifySolutions, Wolfram Language function, https://reference.wolfram.com/language/ref/VerifySolutions.html.

Text

Wolfram Research (1988), VerifySolutions, Wolfram Language function, https://reference.wolfram.com/language/ref/VerifySolutions.html.

CMS

Wolfram Language. 1988. "VerifySolutions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VerifySolutions.html.

APA

Wolfram Language. (1988). VerifySolutions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VerifySolutions.html

BibTeX

@misc{reference.wolfram_2026_verifysolutions, author="Wolfram Research", title="{VerifySolutions}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/VerifySolutions.html}", note=[Accessed: 15-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_verifysolutions, organization={Wolfram Research}, title={VerifySolutions}, year={1988}, url={https://reference.wolfram.com/language/ref/VerifySolutions.html}, note=[Accessed: 15-November-2026]}