Determine if Continuous x^2-5y^2=6

Determine if Continuous x^2-5y^2=6
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify each term.
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Move the negative in front of the fraction.
Dividing two negative values results in a positive value.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Combine the numerators over the common denominator.
Rewrite as .
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Combine using the product rule for radicals.
Reorder factors in .
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set the radicand in greater than or equal to to find where the expression is defined.
Solve for .
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Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Add to both sides of the inequality.
Take the square root of both sides of the inequality to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the portion of the solution.
The complete solution is the result of both the positive and negative portions of the solution.
or
or
or
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Since the domain is not all real numbers, is not continuous over all real numbers.
Not continuous
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Name

Name one hundred one million eight hundred thirty-four thousand eight hundred forty

Interesting facts

  • 101834840 has 64 divisors, whose sum is 415463904
  • The reverse of 101834840 is 048438101
  • Previous prime number is 137

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 29
  • Digital Root 2

Name

Name six hundred four million six hundred fifty-one thousand five hundred seventy

Interesting facts

  • 604651570 has 8 divisors, whose sum is 1088372844
  • The reverse of 604651570 is 075156406
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7

Name

Name two billion eighty-four million nine hundred ninety-two thousand two hundred thirty-nine

Interesting facts

  • 2084992239 has 32 divisors, whose sum is 3105423360
  • The reverse of 2084992239 is 9322994802
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3