Find the three number in arithmetic progression whose sum amd product are 6 and 6
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a +a+d+a+2d=6
3a+3d=6
a+d=2
a=2-d
Also
a(a+d)(a+2d)=6
(2-d)(2-d+d)(2-d+2d)=6
(2-d) (2)(2+d)=6
(2-d)(2+d)=3
4-d^2=3
d^2=1
d=±1
if d=1 then a=1
then three terms =1,2,3
if d=-1 then a=3
now three terms=3,2,1
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