Let T be the tension in the ideal string and 'a' be the acceleration of the blocks at the instant of release. For the block on the left, the upward acceleration may be found from
T + k₁x – mg = ma
For the block on the right, the downward acceleration may be found from
k₂x + mg – T = ma
Adding the equations gives the acceleration of the blocks as
a = (k₁ + k₂)x/(2m)
However, substracting the equations gives
T = mg – (k₁ – k₂)x/2
for maximum value of k₁ T will be zero.
$\mathrm{mg}=\left(\frac{{\mathrm{k}}_1-{\mathrm{k}}_2}{2}\right)\mathrm{x}$
k₁ = 300