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
Divide Rs. 1290 in to A, B and C such that A is `2/5` of B and B : C = 4 : 3.
If (3x – 4y) : (2x – 3y) = (5x – 6y) : (4x – 5y), find x : y.
If r2 =pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
Which is greater 4: 5 or 19: 25.
Express the given ratio in its simplest form: `6 1/4 : 12 1/2`
Find the fourth proportional of 3, 12 and 4
In winter, a school opens at 10 a.m. and closes at 3.30 p.m. If the lunch interval is of 30 minutes, find the ratio of lunch interval to total lime of the class periods.
Find the ratio of the first quantity to the second.
1 litre, 250 ml
Which pair of ratios are equal? And why?
`2/3, 4/6`
In the ratio 7 : 11, which term is called the consequent?
