Advertisements
Advertisements
Question
If a : b : : c : d, then prove that
2a+7b : 2a-7b = 2c+7d : 2c-7d
Advertisements
Solution
2a+7b : 2a-7b = 2c+7d : 2c -7d
`"a"/"b" = "c"/"d"`
Multiplying both sides by `2/7`
`=> "a"/"b" xx 2/7 = "c"/"d" xx 2/7`
`=> (2"a")/(7"b") = (2"c")/(7"d")`
Applying componendo and dividendo,
`(2"a" + 7"b")/(2"a" - 7"b") = (2"c" + 7"d")/(2"c" - 7"d")`
Hence, 2a+7b : 2a-7b = 2c+7d : 2c-7d
APPEARS IN
RELATED QUESTIONS
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
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.
If p, q and r in continued proportion, then prove the following:
(p2 - q2)(q2 + r2) = (q2 - r2)(p2 + q2)
Find the mean proportion of: 8.1 and 2.5
Verify the following:
108 : 72 : : 129 : 86
A given quantity of rice is sufficient for 60 persons for 3 days. How many days would the rice last for 18 persons?
If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.
Find the missing number in the box in the proportion:
`square/45 = 16/40 = 24/square`
If `(a + b)^3/(a - b)^3 = 64/27`
- Find `(a + b)/(a - b)`
- Hence using properties of proportion, find a : b.
If x, y and z are in continued proportion, Prove that:
`x/(y^2.z^2) + y/(z^2.x^2) + z/(x^2.y^2) = 1/x^3 + 1/y^3 + 1/z^3`
