Advertisements
Advertisements
प्रश्न
If a: b with a ≠ b is the duplicate ratio of a + c: b + c, show that c2 = ab.
Advertisements
उत्तर
The duplicate ratio of
`a/b = ((a + c)^2)/((b + c)^2)`
⇒ `a/b = (a^2 + c^2 + 2ac)/(b^2 + c^2 + 2bc)`
⇒ ab2 + ac2 + 2abc = a2b + bc2 + 2abc
⇒ ac2 - bc2 = a2b - ab2
⇒ c2(a - b) = ab(a - b)
Hence, c2 = ab.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the duplicate ratio of the following :
`sqrt 10 : sqrt 14`
The angles of a triangle are in the ratio 3 :2 : 7. Find each angle.
Which of the following numbers are in continued proportion:
15, 45 and 48
Find the compounded ratio of: (a – b) : (a + b), (a + b)2 : (a2 + b2) and (a4 – b4) : (a2 – b2)2
If y (3x – y) : x (4x + y) = 5 : 12. Find (x² + y²) : (x + y)².
If a : b = 3 : 5, find (3a + 5b): (7a – 2b).
The length and breadth of a window are in 1m and 70 cm respectively. The ratio of the length to the breadth is _______________
To find the ratio of two quantities, they must be expressed in _____ units.
Find the ratio of the following:
30 minutes to 1.5 hours
Express `16 2/3%` as a ratio in the lowest form.
