Advertisements
Advertisements
Question
If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a2 + b2 + c2
Advertisements
Solution
Given that a, b and c are in continued proportion
`=> a/b = b/c => b^2 = ac`
L.H.S = (a + b + c)(a - b + c)
= a(a - b + c) + b(a - b + c) + c(a - b + c)
`= a^2 - ab + ac + ab - b^2 + bc + ac - bc + c^2`
`= a^2 + ac - b^2 + ac + c^2`
`= a^2 + b^2 - b^2 + b^2 + c^2` [∵ `b^2 = ac`]
`= a^2 + b^2 + c^2``
=R.H.S
APPEARS IN
RELATED QUESTIONS
On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?
Mr Kumar borrowed Rs. 15000 for two years. The rates of interest for two successive years are 8% and 10% respectively. If he repays Rs. 6200 at the end of the first year, find the outstanding amount at the end of the second year.
Calculate the amount and the compound interest for the following:
Rs.20, 000 at9°/o p.a. in `2 1/3` years
Calculate the amount and the compound interest for the following:
Rs.25, 000 at `8 2/5 %` p.a. in `1 1/3` years
A sum of Rs. 65000 is invested for 3 years at 8 % p.a. compound interest.
Find the sum due at the end of the first year.
Pooja borrowed Rs 15,000 from Sonali at 11% p.a. compound interest. If she repays Rs 7,550 at the end of first year and Rs 6,101 at the end of second year, find the amount Pooja needs to give to Sonali at the end of third year to clear her debt.
Meera borrowed Rs 12,500 on compound interest from Rajeev for 2 years when the rates of interest for successive years were 8% and 10%. If Meera returned Rs 7,500 at the end of the first year, find the amount she has to return at the end of the second year.
Ramesh saves Rs 4,000 every year and invests it at 10% p.a. compound interest. Calculate his savings at the end of the third year.
Rs.16,000 is invested at 5% compound interest compounded per annum. Use the table, given below, to find the amount in 4 years.
| Year ↓ |
Initial amount (Rs.) |
Interest (Rs.) |
Final amount (Rs.) |
| 1st | 16,000 | 800 | 16,800 |
| 2nd | ........... | ........... | ........... |
| 3rd | ........... | ........... | ........... |
| 4th | ........... | ........... | ........... |
| 5th | ........... | ........... | ........... |
Calculate the amount and the compound interest on:
Rs. 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.
