Question

Find the three numbrs which are in A.P. Sum of these three term is 36 if 5,6,7 be added to numbers
respectively then they become in G.P. So find the number. please urgently ​

Answer 1

Answer:

13,12,11

Step-by-step explanation:

let a-d, a, a+d be the 3 numbers

given

a-d + a + a+d = 36

3a = 36

a = 36/3 = 12

a = 12

also given that (12-d)+5 / (12+6)  = (12+6) / (12+d)+7

=> (17-d)/18 = 18/(19+d)

=> (17-d)(19+d) = 18²

=> 323 +17d - 19d - d² = 324

=> 324-323 +19d - 17d + d² = 0

=> d²+2d+1 = 0

(d+1)² = 0

=> d+1=0

=> d = -1

so the 3 numbers are

(12- (-1)) , 12 , 12+ (-1)

12+1 , 12 12-1

13,12,11

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verifiy:  13+5 / 12+6  = 12+6/ 11+7

=> 18/18  = 18/18

=> 1 = 1

verified

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