SOLUTION: Three numbers are in the ratio 2:5:8 . If 10 is added to the middle number, the number form a G P. Find the numbers? Plz help me solve this problem.
Question 852499: Three numbers are in the ratio 2:5:8 . If 10 is added to the middle number, the number form a G P. Find the numbers? Plz help me solve this problem. Found 2 solutions by dkppathak, ewatrrr:Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website! three numbers in ratio 2:5:8
let these numbers are 2x:5x:8x
as per given conditions if 10 is added to middle number
number forms GP(if a,b,c are GP than b^2=ac)
2x,5x+10,8x
(5x+10)^2=2x multiplied by 8x
25x^2+100x+100=16x^2
9x^2+100x+100=0
9x^2+90x+10x+100=0
9x(x+10)+10(x+10)=0
(x+10)(9x+10)=0
x=-10 or x=-10/9
neglecting n second value as it can not be fractional we consider x=-10
numbers are 2x:5x:8x
=-20:-50:-80
verification
(-50+10)^2= -20 multiplied by -80
1600=1600
verified Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi,
Let x represent the constant of proportionality
If 10 is added to the middle number, the number form a G P.
⇒
9x^2 + 100x + 100 = 0
(9x + 10)(x + 10) = 0, x = -10
Numbers are; -20, -50, - 80
and
{ -20, (-50+ 10), - 80 } is {-20, -40, -80} a G.P