If the 4th  term in the expansion of 2+3x1810 has the maximum numerical value, then the range of values of x for which this will be true is

T4 is the numerically greatest term T4 T3≥1, T4 T5≥1⇒T4 T3≥1, T5 T4≤1we have T4 T3=C3   10273x83C2   10283x82=x2,T5 T4=C4   10263x84C3   10273x83=21x64 Now T5 T4≤1⇒21x64≤1⇒x≤6421⇒x∈-6421,6421 →1Also T4 T3≥1⇒x2≥1⇒x≥2⇒x≤-2 or x≥2 →2By 1 and 2 we have x∈-6421,-2∪2,6421