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
Express the given ratio in its simplest form: `1 1/3:2 1/4:2 1/2`
A rectangular field is 100 m by 80 m. Find the ratio of length to its breadth.
Find the value of x, when 2.5 : 4 = x : 7.5.
Which ratio is smaller:
`7/15` or `15/32`
Are the following numbers in proportion 32, 40, 48 and 60?
Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the ratio of Shubham’s mother’s age today to his father’s age today.
Two numbers are in the ratio 11 : 12 and their sum is 460. Find the numbers.
A ratio expressed in lowest form has no common factor other than ______ in its terms.
See the figure and find the ratio of number of circles to all the figures inside the rectangle.
