Find three numbers whose sum is 20.905
Answers
Step-by-step explanation:
Let the three numbers be a,ar,ar
2
.
Given that sum is 52.
∴a+ar+ar
2
=52
⇒a(1+r+r
2
)=52⟶(1)
Sum of product of numbers in pairs is 624.
∴a.ar+ar.ar
2
+ar
2
.a=624
⇒a
2
r(1+r
2
+r)=624
From eq
n
(1), we have
ar=
52
624
=12
⇒a=
r
12
Substituting the value of a, in eq
n
(1), we have
r
12
(1+r+r
2
)=52
⇒3+3r+3r
2
=13r
⇒3r
2
−10r+3=0
⇒3r
2
−9r−r+3=0
⇒(r−3)(3r−1)=0
⇒r=3 or
3
1
For r=3,
a=
r
12
=4
Required numbers are 4, 12, 36.
For r=
3
1
,
a=
r
12
=36
Required numbers are 36,12,4.
Answer:
a.ar+ar.ar2+ar2.a=624
⇒a2r(1+r2+r)=624
From eqn(1), we have
ar=52624=12
⇒a=r12
Substituting the value of a, in eqn(1), we have
r12(1+r+r2)=52
⇒3+3r+3r2=13r
⇒3r2−10r+3=0
⇒3r2−9r−r+3=0
⇒(r−3)(3r−1)=0
⇒r=3 or 31
For r=3,
a=r12=4
Required numbers are 4, 12, 36.
For r=31,
Step-by-step explanation:
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