Does this math problem make sense?

Question

W/o going into imaginary numbers:

If s^2 * t^-2 = 1 and st= -4, what is the value of s+t?

(the asterik means multiply)

Answer 1

well for s^2 * t^-2 = 1 to get 1 s and t 's abs value must be the same so s and t are either equal to 2 or -2
st = -4 shows us that both 2 and -2 are present otherwise it would be positive 4
so s+t must be equal too 0

Answer 2

S +t=0

Answer 3

s^2/t^2 = 1
so
s/t = +-1
so
s = +-t
then
st = -4
so either
s^2 = -4 so s = +-2i and t = +-2i then (s + t) = +-4i
or
-s^2 = -4 so s = +-2 and t = -+2 then (s + t) = 0

Note there are four solutions for s and t since it is an order 4 equation. If you want to ignore imaginary numbers the answer
is zero, but really there are two solutions for what s + t is
(factor the equation):

s^2/t^2 = 1 means s^2 - t^2 = 0
or
(s + t)(s - t) = 0
given your condition st=-4
s + t = 0 gives the real solution and
s - t = 0 gives the imaginary solution
(note the opposite sign implication in the constraint
st = -4 suggests an imaginary solution since s - t = 0 is
a solution). Sorry for using imaginaries, but it is part of the
answer.

Answer 4

I think the given conditions are impossible. You say s^2*t^2 = 1.
This is the same as (s*t)^2 = 1, or s*t = +/- 1; but the second equation says s*t = -4 These are not consistent. The problem does not make sense.

Edit: Sorry misread the equation. Did not see the - in the exponent of t. Disregard my answer.

Answer 5

t^(-2) is the same as 1/t^2, so we can write s^2 * t^(-2) = 1 as:

(s^2)/(t^2) = 1.
Multiply both sides by t^2
s^2 = t^2
Take the square root of both sides.
|s| = |t| (absolute value of s = absolute value of t)
s * t = -4
Since this is a negative number, we know that s = -t (since negative times a positive is a negative).
So we substitute that in:
s * (-s) = -4
-(s * s) = -4
s * s = 4
.: s = +/- 2 and t = -s.

so s + t = -2 + 2 or 2 + -2, which equals 0.

Answer 6

I think s + t = 0, and s= 2 and t= -2. When squared and divided, they would equal 1. When multiplied, they would create -4.

Answer 7

No. As written, s^2 = t^2 from the first equation. Meaning s = t or s = -t. Note, 's' does not equal -4/t as implied by the second equation. The inconsistency makes the problem unsolvable in the sense that you'd be familiar with.

Answer 8

(s^2)(t^-2) = 1
(s^2)/(t^2) = 1
s^2 = t^2

there for |s| = | t |

st = -4

ss = -4 (cos |s| = |t| so assume s = t now)
s^2 = -4
s = (-4)^-2

but its not possible to get the square root of a negative number like -4, we will just get the square root of 4

so s = 2

well, multiplication, to get a negative number, one have to be negative and the other has to be possible

so if s = 2 then t must be -2


s + t = 2 + (-2) = 0


....Did I get it right??




=)



Peace*

Answer 9

it doesn't makes sense because it's contradictory. -4*-4 is 16 not 1, and s^2*t^2= s*t*s*t = st*st.

Answer 10

s^2 * t^-2 = 1 -----> (s/t)^2 = 1
st = -4 ----> t = -4/s


(s / (-4/s))^2 = 1
(s^2/-4)^2 = 1
(s^4/16) = 1
s^4 = 16
s = +/- 2

t = -/+ 2

s + t = (-2 - 2) or (2 + 2) or (2 - 2)
=-4 or 4 or 0