The sum of $3$ numbers in a geometric sequence is $175.5$:
$$b_1 + b_2 + b_3 = 175.5$$
And the product of the same numbers is $91125$:
$$b_1 \cdot b_2 \cdot b_3 = 91125$$
I used the formula for the product and calculated $b_2$ which equals to $45$, but when I try to calculate the other terms I get stuck with this formula and I am not sure if the formula I get is correct:
$$45q^2 - 130.5q + 45 = 0$$
Thanks in advance
Let the three numbers be $\frac ar, a, ar$.
Product: $$\frac ar\cdot a\cdot ar=91125\\ a^3=91125\\ a=45$$
Sum: $$45 (\frac 1r+1+r)=175.5\\ r^2-2.9r+1=0\\ (r-2.5)(r-0.4)=0\\ r=0.4, 2.5$$
Hence the numbers are either $$18,45,112.5$$ or $$112.5,45.18$$.