(a) Find the two numbers such that the mean proportion between them is 9 and the third proportion to them is 243.
Answers
Answered by
3
The number are 3 and 27
Total numbers = 2 = a and b (Given)
Mean proportion = 9 (Given)
Third proportion = 243 (Given)
Thus,
ab = 9²
ab = 81
= a = 81/b --- 1
As a,b,243 are in proportion , thus
= a/b = b/243
= a(243) = b ²
=>(81/b)(243)=b². Using (1)
= ( 3^4/b)(3^5)=b^2
= 3^9 =b^3
= 3^3 =b
= 27 = b
From ab = 81, substituting the value -
= a(27 )=81.
From b = 27
= a=3
Therefore the numbers are 3 and 27
The greatest number is 27
Similar questions