Advertisements
Advertisements
प्रश्न
If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`
Advertisements
उत्तर
∵ a, b, c, d are in proportion
`a/b = c/d` = k(say)
a = bk, c = dk.
L.H.S. = `(a^2 + ab)/(c^2 + cd)`
= `(k^2b^2 + bk.b)/(k^2d^2 + dk.d)`
= `(kb^2(k + 1))/(d^2k(k + 1)`
= `b^2/d^2`
R.H.S. = `(b^2 - 2ab)/(d^2 - 2cd)`
= `(b^2 - 2.bkb)/(d^2 - 2dkd)`
= `(b^2(1 - 2k))/(d^2(1 - 2k)`
= `b^2/d^2`
∴ L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Using properties of proportion, solve for x:
`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`
If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n
Find the value of the unknown in the following proportion :
c
If ( a+c) : b = 5 : 1 and (bc + cd) : bd = 5 : 1, then prove that a : b = c : d
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
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.
If 57 : x : : 51 : 85, then the value of x is
If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
If x : y = y : z, then x2 : y2 is ______.
