Advertisements
Advertisements
Question
Find the third proportional to a – b and a2 – b2
Advertisements
Solution
Let the third proportional to a – b and a2 – b2 be x.
`=>` a – b, a2 – b2, x are in continued proportion.
`=>` a – b : a2 – b2 = a2 – b2 : x
`=> (a - b)/(a^2 - b^2) = (a^2 - b^2)/x`
`=> x = (a^2 - b^2)^2/(a - b)`
`=> x = ((a + b)(a - b)(a^2 - b^2))/(a - b)`
`=>` x = (a + b)(a2 – b2)
APPEARS IN
RELATED QUESTIONS
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
Find the fourth proportional to 2xy, x2 and y2.
Find the value of the unknown in the following proportion :
c
If x, 12 and 16 are in continued proportion! find x.
If three quantities are in continued proportion, show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Find two numbers whose mean proportional is 18 and the third proportional is 486.
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
If b is the mean proportional between a and c, prove that `(a^2 - b^2 + c^2)/(a^-2 -b^-2 + c^-2)` = b4.
Find the value of x in each of the following proportions:
51 : 85 : : 57 : x
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
