Advertisements
Advertisements
Question
If y is the mean proportional between x and y; show that y(x+z) is the mean p roporti ona I between x2+ y2 and y2+ z2
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.
(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
APPEARS IN
RELATED QUESTIONS
Using properties of proportion, solve for x:
`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`
Given four quantities p, q, r and s are in proportion, show that
q2(p - r) : rs (q - s) =(p2- q2- pq): ( r2-s2-rs).
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
Show that the following numbers are in continued proportion:
48, 60, 75
The length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?
If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).
If a, b, c are in continued proportion, prove that: a : c = (a2 + b2) : (b2 + c2)
7 Persons is to 49 Persons as 11 kg is to 88 kg
A particular high school has 1500 students 50 teachers and 5 administrators. If the school grows to 1800 students and the ratios are maintained, then find the number of teachers and administrators
Determine if the following are in proportion.
24, 28, 36, 48
