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b can be equal to 3 or 4:
25*3*3 - 3*3*3*3 = 225 - 81 = 144.
25*4*4 - 4*4*4*4 = 400 - 256 = 144.
That is correct. I knew it was 3 and 4.
But I need the method by which one can calculate the answer.
Thank you.
You can rearrange the terms set this up as a quadratic equation and solve for b2
Let x = b2, then
25b2 - b4 = 144 can be rewritten as
-x2 + 25x -144 = 0, and a = -1, b = 25, and c = -144
Plugging into the quadratic equation, we get:
x = (-25 +/- sqrt(25^2 - 4*-1*-144)) / 2*-1
x = (-25 +/- sqrt(625 - 576) ) / -2
x = (-25 +/- 7) / -2
x = -18/-2 = 9, or
x = -32/-2 = 16
and since x = b2, then b = 3 or 4
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