Question

If 1/84 = 4²s-1× 162s², what is the value of s?
1) -1
2) 1
3) no solution

Answer 1

The value of s in the equation 1/84 = 4²s-1× 162s² is 12.

Step-by-step explanation:

This is an equation in one variable, so we should be able to solve for the unknown value. This expression may look formidable, but first we can simplify the denominator and write it as a perfect square as well:

1/84 = 16s-1 * (9s2)

Now we can rewrite it as:

1/84 = 144s / (16s2)

To simplify further, we can multiply both the numerator and the denominator by 84:

1 = 12s / s2

Now we can multiply through by s2 to get a quadratic equation:

s2 = 12s

Finally, we can solve this quadratic equation:

s2 - 12s = 0

Factoring out s, we get:

s(s - 12) = 0

So, s = 0 or s = 12. However, since we cannot divide by 0, the only valid solution is s = 12.