Equations with Exponents

[santhosh.iipm]

Given that 5 - square root of y^2 = -3. what is Y? ( Guide 3 - Equations,In Equalities & VICs,Chapter 2 - pg:35 - problem 5)

5 - square root of y^2 = -3.
5-y=-3
y=8.

If y^2 =25 then y = 5 or -5.
Square root of 25 = 5.Similarly,Square root of y^2 = y.

However, in the guide answer is given as 8 and -8.Both 8 and -8 satisfies the equation but generally we consider only positive values for even roots.So can y take the value -8?

For example,Square root of 25 can be written as Square root of (-5)^2 or Square root of (5)^2 in which case Square root of 25 will be 5 or -5 but we always consider only positive value for even roots so Square root of 25 is 5.

[frederickmevans]

5 - sqrt(y^2) = -3
-sqrt(y^2) = -8
sqrt(y^2) = 8
y^2 = 64
y = 8 or -8 because the even root of a positive number can be positive or negative. Do NOT assume only the positive root because if you see a Data Sufficiency question which says
"What is x?"
and statement 1 is x^2 = 4
you do NOT know whether x = 2 or -2 and therefore this statement alone is insufficient to answer the question. if statement 2 said x^3 = -8
however, you would know x = -2 because odd roots have only one value.

[jnelson0612]

Great work Frederick!