SOLUTION: Solve y to the second power equals twenty-five , where y is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with comm

Algebra ->  Testmodule -> SOLUTION: Solve y to the second power equals twenty-five , where y is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with comm      Log On


   

Question 1208686: Solve y to the second power equals twenty-five , where y is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

They want you solve  

    y%5E2 = 25.


Take square root of both sides

    y = +/- sqrt%2825%29 = +/- 5.


The original equation has two roots. 

One root is y= 5.

Another root is y= -5.


CHECK.  5%5E2 = 25.       ! correct !

        %28-5%29%5E2 = 25.    ! correct !


ANSWER.  The original equation has two solutions:  y = 5  and  y = -5.

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The tutor ikleyn has a great answer. Here's another approach
y%5E2+=+25

y%5E2-25+=+0

%28y-5%29%28y%2B5%29+=+0 Difference of squares factoring rule a^2-b^2 = (a-b)(a+b)

y-5=0 or y%2B5+=+0 If A*B = 0 then either A = 0 or B = 0

y+=+5 or y+=+-5

To check each answer, plug them into the original equation one at a time.
Make sure the negative is being squared as well.
If y = -5 then y%5E2+=+%28-5%29%5E2+=+%28-5%29%2A%28-5%29+=+25 and NOT y%5E2+=+-%285%5E2%29+=+-1%2A5%2A5+=+-25