Find the value of $a$ and $b$ when value of $x\cdot y \cdot z$ is given for both conditions If $a,x,y,z,b$ are in $Arithmetic$ $Progression$ then the value of $x\cdot y \cdot z$ is $\frac{35}{3}$ and if they are in $Harmonic$ $Progression$ then the value of $x\cdot y \cdot z$ is $\frac{75}{7}$, where $a$ and $b$ are given positive integers. Find $a \cdot b$
I am not able to initiate this problem. Could someone give me slight hint to initiate this problem?

Hint: Due to symmetry reasons it is convenient to use the middle variable $y$ as center of  the arithmetic and geometric progression. 

We obtain
  \begin{array}{c|c|c|c|cl}
a&x&y&z&b\qquad&\qquad   x\cdot y\cdot z\\
\hline
y-2k&y-k&y&y+k&y+2k\qquad&\qquad(y-k)\cdot y\cdot (y+k)=\frac{35}{3}\\
yq^{-2}&yq^{-1}&y&yq&yq^2\qquad&\qquad yq^{-1}\cdot y\cdot yq=\frac{75}{7}
\end{array}
So, we have to solve the equations
  \begin{align*}
y(y^2-k^2)&=\frac{35}{3}\\
y^3&=\frac{75}{7}
\end{align*}

