Find the solutions to: | x squared + 1 | = 5?

Question

Find the solutions to: | x squared + 1 | = 5?

Answer 1

2, -2, square root of 6 times i, negative square root of 6 times i

Answer 2

|x^2 + 1|= x^2+1  

thus,

     x^2+1 = 5

or, x^2 = 4

or, x = 2    

                that's it.

Answer 3

X2 + 1 = 5

X2=4

X=+or-2

-X2-1 = 5

X2 = -6

X= + or - square root of 6

Answer 4

| x squared + 1 | = 5

x^2 + 1 = + 5 and - 5

x^2 = -1 + 5  and -1 + -5

x^2 = -6, 4

x = -6 (no real sol'n)   ,  x = √4

x= 2

SS = {, 2}

Answer 5

x² + 1 = 5

x² = 4

x = ± 2

x² + 1 = - 5

x² = - 6

x = 6 i²

x = ± √6 i

Answer 6

2 is the answer

Answer 7

|xˆ2 + 1| = 5

This has two solutions because it is an absolute value.

Solution #1:

xˆ2 + 1 = 5

xˆ2 = 5 - 1

xˆ2 = 4

√(xˆ2) = √(4)

x = 2 (<==ANSWER #1)

Solution #2:

xˆ2 + 1 = -5

xˆ2 = -5 - 1

xˆ2 = -6

√(xˆ2) = √(-6)

x = -√6 (<==ANSWER #2)

Hope I helped!

Answer 8

the answer is not just '2'.  the answer is x=2 OR -2

the ||s mean 'absolute value', so you must consider negatives.

2x2+1=5 AND -2x-2=5

Answer 9

2

Answer 10

x = 2 or -2

Answer 11

x is 2

Answer 12

the modulus signs means all the solutions to:

x^2 + 1 = 5

OR

- (x^2 + 1) = 5

so the solution set is all the solutions to the first equation, and all the solutions to the second equation.

The solutions to the first equation:

x^2 + 1 = 5

x^2 = 4

x = +- 2

The solutions to the second equation:

- (x^2 + 1) = 5

x^2 + 1 = -5

x^2 = -6

There are no solutions to this equation since no real number squared can result in a negative number.

So the solution set is:

{-2, 2}

-√6 is not a solution for this is because √-6 does NOT equal -√6.  ÃƒÂ¢Ã‚ˆÂš-6 is an imaginary number and i dont think u are expected to include this in your solution set.

Answer 13

  There are three solutions and they are 2, -2 and i*sqrt(6).  

As x squared + 1  is within abs the sign can be negative or positive. If

x squared + 1 is positive, then it is = 5.  So,

x squared = 5-1 = 4. So

x = plus or minus root 4

So x = -2 or 2.

If x squared +1 is negative, then it is = -5. So

x squared = -5 -1 = -6. So

x = sqrt(6)*sqrt(-1).

=> i*sqrt(6).

S.S  =  {-2, 2, i*sqrt(6)}

I hope this is clear.