Advertisements
Advertisements
प्रश्न
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Advertisements
उत्तर
Let the quantity to be added be x.
Then
`((a + b) + x)/((a - b) + x) = (a + b)^2/(a - b)^2`
⇒ (a + b) (a - b)2 + (a - b)2.x
= (a + b)2 (a - b) + (a + b)2.x
⇒ [(a + b)2 - (a - b)2]x
= (a2 - b2) (a - b) - (a2 - b2) (a + b)
⇒ (4abx) = (a2 - b2) [(a - b) - (a + b)]
⇒ x = `(-2b(a^2 - b^2))/(4ab) = (b^2 - a^2)/(2a)`.
APPEARS IN
संबंधित प्रश्न
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx2 – 2ax + 3b = 0.
Find the value of x in the following proportions : 3 : x = 24 : 2
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`
3 : 5 : : `square` : 20
Sleeping time of a python in a 24 hour clock is represented by the shaded portion in the following figure.
The ratio of sleeping time to awaking time is ______.
Determine if the following are in proportion.
32, 48, 70, 210
Write True (T) or False (F) against the following statement:
5.2 : 3.9 : : 3 : 4
The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.
