let u,v,w be real numbers in geometric progression such that u>v>w.suppose u^40=v^n=w^60
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since u,v,w in gp,u/v=v/w=r(say)
=>v=wr and u=vr=wr^2
thus u^40=w^60
=>w^40×r^80=w^60
=>r^80=w^20=>w=r^4=>r=w^(1/4)
now,v^n=w^60=>w^n×r^n=w^60=>w^n×w^(n/4)=w^60
=>w^(n+n/4)=w^60
=>5n/4=60=>n=240/5=48
thus n=48
=>v=wr and u=vr=wr^2
thus u^40=w^60
=>w^40×r^80=w^60
=>r^80=w^20=>w=r^4=>r=w^(1/4)
now,v^n=w^60=>w^n×r^n=w^60=>w^n×w^(n/4)=w^60
=>w^(n+n/4)=w^60
=>5n/4=60=>n=240/5=48
thus n=48
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