Finding three geometrically numbers knowing that their sum is greater than 78 and 30 units exceeds the sum of the other two.
strange wording ....
" Finding three geometrically numbers"
I assume you have 3 numbers in a geometric sequence.
"30 units exceeds the sum of the other two"
...... which "other two" , the first two, the last two , or the middle two ?
the three numbers are:
a, ar, and ar^2
a + ar + ar^2 > 78
I will assume that 30 exceeds the sum of the first two
30 > a + ar
a(1+r) < 30 and a(1+r + r^2) > 78
I will continue once you clarify your question.