Advertisements
Advertisements
Question
If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2 + y2 and y2 + z2.
Advertisements
Solution
Since y is the mean proportion between x and z
Therefore, y2 = xz
Now, we have to prove that xy + yz is the mean proportional between x2 + y2 and y2 + z2,
i.e., (xy + yz)2 = (x2 + y2)(y2 + z2)
LHS = (xy + yz)2
= [y(x + z)]2
= y2(x + z)2
= xz(x + z)2
RHS = (x2 + y2)(y2 + z2)
= (x2 + xz)(xz + z2)
= x(x + z) z (x + z)
= xz(x + z)2
LHS = RHS
Hence, proved.
APPEARS IN
RELATED QUESTIONS
If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2 + 11n^2)`
a, b, c are in continued proportion. If a = 3 and c = 27 then find b.
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.
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Find the third proportional to:
x - y, x2 - y2
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
Choose the correct answer from the given options :
The mean proportional between `(1)/(2)` and 128 is
If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.
