Let s and t be any two whole numbers, excluding 0.
True or false.
The statemnt s/t = t/s is always true?
What did you do first to answer this question?
s/t=t/s <=> s²=t² <=> s=±t
We were told that s and t are any integer such that s≠0 and t≠0.
So the statement "s/t=t/s is always true" is false.
what did you do first to answer the question?
s/t=t/s <=> s²=t² <=> s=±t
That is to find the conditions under which the statement is true. As you probably know, the statement is true at times, but not all the time.
The first line says that the statement is true if and only if s is equal to +t or -t.
The sign <=> means "equivalent to"
To answer this question, we need to analyze the given statement, s/t = t/s, and determine if it is always true or not for any values of s and t (excluding 0).
First, we need to recall the basic property of division, which states that dividing a number by another number is the same as multiplying by the reciprocal of the second number. So, s/t can also be written as s * (1/t), and t/s can be written as t * (1/s).
Next, we can simplify the given statement by multiplying s/t and t/s using the reciprocals:
s/t = s * (1/t)
t/s = t * (1/s)
Now, we can observe that if we multiply both sides of the equation by t * s, the reciprocal terms will cancel out:
(s * (1/t)) * (t * s) = (t * (1/s)) * (t * s)
s * (1/s) = t * (1/t)
The left side simplifies to 1, as any number multiplied by its reciprocal equals 1. The right side also simplifies to 1. Therefore, the statement simplifies to:
1 = 1
Since this equation is always true, we can conclude that the statement s/t = t/s is always true for any two whole numbers (excluding 0).