Advertisements
Advertisements
प्रश्न
If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.
उत्तर
∵ b is the mean proportional between a and c, then,
b² = a × c ⇒ b² = ac …(i)
Now a, c, a2 + b2 and b2 + c2 are in proportion
if `a/c = (a^2 + b^2)/(b^2 + c^2)`
if a(b2 + c2) = (a2 + b2)
if a(ac + c2) = c(a2 + ac) ...[from (i)]
if ac(a + c) = a2c + ac2
if ac(a + c) = ac(a + c)
which is true.
Hence proved.
APPEARS IN
संबंधित प्रश्न
Find the mean proportional to (x – y) and (x3 – x2y).
Check whether the following numbers are in continued proportion.
2, 4, 8
Find the fourth proportional to:
2xy, x2, y2
If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.
Write (T) for true and (F) for false in case of the following:
81 kg : 45 kg : : 18 men : 10 men
Show that the following numbers are in continued proportion:
16, 84, 441
The cost of 18 chairs is Rs 22770. How many such chairs can be bought for Rs 10120?
Fill the boxes using any set of suitable numbers 6 : `square` : : `square` : 15
A recipe calls for 1 cup of milk for every `2 1/2` cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people?
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
2 kg : 80 kg and 25 g : 625 g
