the sum of the 3 nos in ap is 18 if the prod of first and the third term is 5 times tge common difference find the 3 nos
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s3=3\2(a+2d)
18=3\2×2(a+d)
18\3=a+d
a+d=6
a=6-d
a(a3)=5d
a(a+2d)=5d
(6-d)(6-d+2d)=5d
(6-d)(6+d)=5d
(6^2-d^2)=5d
36-d^2=5d
5d+d^2-36=0
d^2+5d-36=0
d^2+9d-4d-36=0
d(d+9)-4(d+9)=0
(d+9)(d-4)=0
d=-9 or d=4
if d=4
a=6-4
Ap→2,6,10
if d=-9
a=6-(-9)=15
Ap→15,6,-3
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Answer:
Step-by-step explanation:
assume the no.s to be (a-d),a,(a+d)
(a-d)+a+(a+d)=18
3a=18
a=6 ......................(1)
product: (a-d)(a+d)=5d
a^2-d^2=5d
36-d^2=5d
d^2+5d-36=0
by splitting middle term,
(d+9)(d-4)=0
thus, d=4 or -9
with d=4 : solutions 2,6,10
with d=(-9) : solutions 15,6,-3
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