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Find four proportionals such that the sum of the extremes is 21, the sum of the means 19, and sum of the squares of all the four numbers is 442.

Find four proportionals such that the sum of the extremes is 21, the sum of the means 19, and sum of the squares of all the four numbers is 442.

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
Let the numbers be a,b,c,d
From given a+d=21 and b+c=19
a2+b2+c2+d2=442
As they are in proportion ad=bc
When ratio of 2 terms=ratio of 2 other terms they are in proportion
So (a2+d2+2ad)+(b2+c2+2bc)=441+361
442+4ad=802
ad=90 So ad=bc=90
(a-d)2=(a+d)2-4ad=441-360=81
So a-d=9 and a+d=21
So a=15 d=6
Similarly (b-c)2=361-360=1
So b-c=1 and b+c=19 So b=10,c=9
So Four proportionals are 15,10,9,6

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