three numbers whise sum is 15 are is A.P.if 1,4,19 be added to them respectively the resulting numbers are in G.P. find the numbers
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Step-by-step explanation:
let numbers be a- b ,a and a + b
a- b + a + a + b = 15
3a = 15
a=5
ATQ
a-d+1 , a+4 , a+d+19 :are in GP
b^2=ac
(a+4)^2=(a-d+1)(a+d+19)
=> a2+16+8a=a2+ad+19a-ad-d2-19d+a+d+19
=> 16+8a=19a- d2 - 19d + a + d + 19
put value of a
=> 56=95-d2-18d+119=0
=> d2+18d-63=0
=>(d-3)(d+21)=0
=>d=3, -21
a-d =5-3=2 5+21=26
a =5. or 5
a+d=5+3=8 5-21= -16
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