Exp. (b)Given, m is the AM of l and n∴l+n=2mand G1​,G2​,G3​ are geometric means between l and n∴l,G1​,G2​,G3​,n are in GP.Let r be the common ratio of this GP.∴G1​=lrG2​=lr2G3​=lr3n=lr4r=(ln​)41​ Now,G14​+2G24​+G34​=(lr)4+2(lr2)4+(lr3)4=l4×r4(1+2r4+r8)=l4×r4(r4+1)2=l4×ln​(ln+l​)2=ln×4m2=4lm2n