Advertisements
Advertisements
Question
If `"a"/"b" = "c"/"d"`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = ("a" + "c")^4/("b" + "d")^4`
Advertisements
Solution
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
RELATED QUESTIONS
If 5x + 6y : 8x + 5y = 8 : 9, find x : y.
There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How any more girls should be added to the council so that the ratio of the number of boys to the number of girls may be 9 : 5?
Find the fourth proportional of 4 hours 40 minutes, 1 hour 10 minutes and 16 hours.
Find the triplicate ratio of 13 : 23
Find the ratio of:
150 mL to 2 L
If a : b = 9 : 10, find the value of `(2a^2 - 3b^2)/(2a^2 + 3b^2)`
In a box, the ratio of red marbles to blue marbles is 7 : 4. Which of the following could be the total number of marbles in the box?
In the following figure, find the ratio of the area of the shaded portion to that of the whole figure:
Find the ratio of the following:
40 cm to 1.5 m
Given below is a Mathematical term.
Find the ratio of consonants to vowels in the term.
