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 a : b = 3 : 5, find: (10a + 3b) : (5a + 2b)
Express the given ratio in its simplest form: 200 m : 5 km
Express the given ratio in its simplest form: 3 hours : 1 day
Find the third proportional of 1.6 and 0.8
Express the following ratio in the simplest form:
324 : 144
Ratio of 5 km 400 m to 6 km = _______________
Out of 50 students in a class, 30 are boys. Find the ratio of number of boys to the number of girls
The food labels given below give information about 2 types of soup: cream of tomato and sweet corn. Use these labels to answer the given questions. (All the servings are based on a 2000 calorie diet.)
| Sweet Corn | Cream of Tomato | ||
| Nutrition Facts | Nutrition Facts | ||
| Serving Size 1 cup (240ml) | Serving Size 1 cup (240ml) | ||
| About 2 serving per Container | About 2 serving per Container | ||
| Amount Per Serving | Amount Per Serving | ||
| Calories 90 | Calories from Fat 9 | Calories 100 | Calories from Fat 20 |
| % Daily Value* | % Daily Value* | ||
| Total Fat 2g | 2% | Total Fat 2g | 3% |
| Saturated Fat-0g | 0% | Saturated Fat-1.5g | 6% |
| Cholesterol 0mg | 0% | Cholesterol 10mg | 3% |
| Sodium 540mg | 22% | Sodium 690mg | 29% |
| Total Carbohydrate 17g | 6% | Total Carbohydrate 17g | 6% |
| Dietary Fibre 3 gram | 14% | Dietary Fibre 4 gram | 18% |
| Sugar 5g | Sugar 11g | ||
| Protein 3g | Protein 2g | ||
| Vitamin A 30% | Vitamin C 10% | Vitamin A 20% | Vitamin C 20% |
| Calcium 2% | Iron 6% | Calcium 0% | Iron 8% |
| *Per cent Daily Values are based on a 2,000 calorie diet. |
*Per cent Daily Values are based on a 2,000 calorie diet. |
||
Calculate ratio of calories from fat in sweet corn soup to the calories from fat in cream of tomato soup.
In a year, Ravi earns Rs 360000 and paid Rs 24000 as income tax. Find the ratio of his income to income tax.
In a school, the ratio of the number of large classrooms to small classrooms is 3 : 4. If the number of small rooms is 20, then find the number of large rooms.
