Three positive numbers are in GP. Their product is 216 and their sum is 21. Find the largest number.
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Three positive numbers are in GP. Their product is 216 and their sum is 21. Find the largest number.

G1 Physics · Accepted Answer

Write them as a/r,a,ar. Product=a³=216, so a=6. Then 6/r+6+6r=21 ⇒ 2r²−5r+2=0, giving r=2 or 1/2. The numbers are 3,6,12; largest=12.