Question
If 2x + 4y - 9 = 0, then find the value of 8x 3
- 723 + 64y 3 + 216xy.Solution
2x + 4y - 9 = 0
If, a + b - c = 0, then, a 3 + b 3 - c 3 = - 3abc
So, (2x) 3 + (4y) 3 + ( - 9) 3 = - 3 X (2x) X (4y) X (9)
Or, 8x 3 + 64y 3 - 729 = - 216xy
Or, 8x 3 + 64y 3 - 729 + 216xy = 0 ....(i)
8x 3 - 723 + 64y 3 + 216xy = 8x 3 - 729 + 6 + 64y 3 + 216xy
Put the value of equation (i) in the above equation, we get,
8x 3 - 723 + 64y 3 + 216xy = 0 + 6 = 6
- A person invested Rs. 30,000 in two schemes. One scheme gives a simple interest of 7% p.a., while the other scheme gives 11% p.a. If the total interest ear...
A man invested a certain amount of sum at 12.5% per annum simple interest and earned an interest of Rs.2400 after 4 years. If the same amount is investe...
Simple interest received at the rate of 15% p.a. for 2 years on a principal amount of Rs. 9000 is twice of the simple interest received at 10% p.a. for ...
A sum of money amounts to Rs 5400 in 3 years and to Rs 6000 in 5 years at simple interest. Find the principal and the rate of interest per annum.
A man invested certain sum at simple interest of r% p.a. such that it amounts to 130% of itself in 3 years. Find the interest earned when Rs. 3000 is in...
- An amount was invested at a simple interest rate. After 6 years, it amounted to (126/108) times the amount it had reached in 4 years. What is the rate of i...
An amount of 'a' is invested at an annual interest rate of 18% with simple interest, and another amount of 'a + 750' is invested at an annual interest...
A man invested certain sum at 10% p.a. simple interest for his son who was 17 years old. If the amount received by the son when he was 30 years old is R...
Arjun borrowed Rs. 5000 at R% S.I. and Rs. 6000 at (R + 5)% S.I. for 2 years. The total interest paid was Rs. 2800. Find the rate at which he borrowed R...
A sum of Rs. 3200 is invested at simple interest for 2 years. If the rate interest for first year is 12% p.a. while 20% p.a. for second year, then find ...
Relevant for Exams:
