Advertisements
Advertisements
प्रश्न
If `"a"/"b" = "c"/"d"`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = ("a" + "c")^4/("b" + "d")^4`
Advertisements
उत्तर
Let `"a"/"b" = "c"/"d"` = k
⇒ a = bk and c = dk
L.H.S = `("a"^3"c" + "ac"^3)/("b"^3"d" + "bd"^3)`
= `(("bk")^3 xx ("dk")+("bk")("dk"^3))/("b"^3"d"+ "bd"^3)`
= `("b"^3"k"^3"dk"+"bkd"^3"k"^3)/("b"^3"d"+"bd"^3)`
= `("b"^3"dk"^4+"bd"^3"k"^4)/("b"^3"d"+"bd"^3)`
= `("k"^4("b"^3"d"+"bd"^3))/("b"^3"d"+"bd"^3)`
= k4
R.H.S = `("a" + "c")^4/("b" + "d")^4`
= `("bk"+"dk")^4/("b"+"d")^4`
= `("k"^4("b"+"d")^4)/("b"+"d")^4`
= k4
∴ L.H.S = R.H.S
संबंधित प्रश्न
Find sub-triplicate ratio of 64 : 27
Find the ratio of the following in the simplest fcrm:
432 and 120
If a: b = 4: 7, find the following:
`(5"a" - 4"b")/(2"a" - 3"b")`
Express the given ratio in its simplest form: 1.5 : 2.5
A line is divided into two parts in the ratio 2.5 : 1.3. If the smaller one is 35.1 cm, find the length of the line.
If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z.
If (4x + 3y) : (3x + 5y) = 6 : 7, find y, if x = 27
Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.
In the following figure, division represents 1 cm:
Express numerically the ratios of the following distances:
AG : AD
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of number of students who opted cricket to the number of students opting basketball.
