Advertisements
Advertisements
प्रश्न
If ax = by = cz, prove that
`x^2/(yz) + y^2/(zx) + z^2/(xy) = (bc)/a^2 + (ca)/b^2 + (ab)/c^2`.
Advertisements
उत्तर
Let ax = by = cz = k, then `x = k/a, y = k/b and z = k/c`
L.H.S. = `x^2/(yz) + y^2/(zx) + z^2/(xy)`
= `k^2/(a^2 xx k/b xx k/c) + k^2/(b^2 xx k/c xx k/a) + k^2/(c^2 xx k/a xx k/b)`
= `(bc)/a^2 + (ca)/b^2 + (ab)/c^2`
= R.H.S.
Hence proved.
APPEARS IN
संबंधित प्रश्न
If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.
Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`
If a, 12, 16 and b are in continued proportion find a and b.
If 22.5 m of a uniform iron rod weighs 85.5 kg, what will be the weight of 5 m of the same rod?
35 inland letters cost Rs 87.50. How many such letters can we buy for 315?
If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?
If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?
In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?
Determine if the following are in proportion.
33, 121, 9, 96
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and ₹ 4 : ₹ 50
