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If `x^2 - a = 14` and `x^2+a=16,` what is the value of `a` ?

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timw996 | Student, Grade 10 | Salutatorian

Posted September 27, 2013 at 2:47 PM via web

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If `x^2 - a = 14` and `x^2+a=16,` what is the value of `a` ?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 27, 2013 at 2:50 PM (Answer #1)

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It is given that x^2 - a = 14.

This equation has two variables x and a. x^2 - a can be equal to 14 for infinite number of sets of x and a. It is not possible to determine a unique solution for a from the given equation.

As the equation x^2 - a = 14 has 2 independent variables it is not possible to determine a unique solution for a.

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timw996 | Student, Grade 10 | Salutatorian

Posted September 27, 2013 at 2:51 PM (Answer #2)

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Sorry there is another equation x^2 + a = 16

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degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted September 27, 2013 at 3:03 PM (Answer #3)

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I edited your original question in response to Answer #2.

If you subtract the first equation from the second one, you get `2a=2,` so `a=1.`

Althought it wasn't asked for, you can go further and solve for `x,` and we find that both `+-sqrt(15)` work. Finally, we can check our solution:

`(+-sqrt(15))^2-1=14` and `(+-sqrt(15))^2+1=16,` so it works.

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atyourservice | TA , Grade 10 | Valedictorian

Posted May 31, 2014 at 11:53 PM (Answer #4)

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 and 

combine the problems:

x^2 -a - x^2 -a = 14 - 16

simplify

-2a = -2

divide by -2

a = 1

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givingiswinning | Student, Grade 10 | Valedictorian

Posted August 16, 2014 at 12:12 AM (Answer #5)

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x^2 -a - x^2 -a = 14 - 16

-2a = -2

a = 1

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