Advertisements
Advertisements
Question
If y is the mean proportional between x and z, show that :
xyz (x+y+z)3 =(xy+yz+xz)3
Solution
Since y is the mean proportion between x and z
y2 = xz
LHS
xyz (x + y + z)3
= yy2 (x + y + z)3
= y3 (x + y +z)3
= [y (x + y + z)]3
= (xy + y2 + yz)3
= (xy + y2 + yz)3 = RHS
LHS = RHS
APPEARS IN
RELATED QUESTIONS
If x2, 4 and 9 are in continued proportion, find x.
Using properties of proportion, solve for x:
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
Find the value of the unknown in the following proportion :
3 : 4 : : p : 12
Find the third proportion to the following :
`9/25` and `18/25`
If x, 12 and 16 are in continued proportion! find x.
Find the fourth proportional to:
x3 - y2, x4 + x2y2 + y4, x - y.
If 9, x, x 49 are in proportion, find the value of x.
If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`
Are the following statements true?
40 persons : 200 persons = ₹ 15 : ₹ 75
