4. The difference between two positive numbers is 7 and the difference between thes
cubes is 805. If 'A' represents their product and 'B' represents the sum of their squares,
find the value of 'A-B'.
Answers
Answer:
- 71
Step-by-step explanation:
Let the numbers are x and y. Thus,
A = product of x and y = xy
B = sum of sq. x and sq. y = x² + y²
Given, difference between two positive numbers is 7 and their cubes is 805.
=> x³ - y³ = 805
=> (x - y)(x² + y² + xy) = 805
=> x² + y² + xy = 805/7 = 115 {x - y = 7}
=> B + A = 115 ...(1)
If you meant 'A + B' answer is 115. If not :
Square on both sides of x - y
=> (x - y)² = 7²
=> x² + y² - 2xy = 49
=> B - 2A = 49 ...(2)
Subtract (2) from (1), we get
=> (B + A) - (B - 2A) = 115 - 49
=> 3A = 66
=> A = 22, thus, from (1),
22 + B = 115 => B = 93
Hence, A - B = 22 - 93 = - 71
Given :-
The difference between two positive numbers is 7 and the difference between these cubes is 805. If 'A' represents their product and 'B' represents the sum of their squares,
To Find :-
A - B
Solution :-
So,
Let the number be n and m
A = n × m = nm
B = n² + m² = (n + m)²
Now
n³ - m³ = 805
(n - m) (n² + m² + nm) = 805
Since difference is 7
7 × n² + m² + nm = 805
n² + m² + nm = 805/7
n² + m² + nm = 115
(n² + n) + (m² + m) = 115
A + B = 115
Now
On squaring the first eq.
(n - m)² = (7)²
(n - m)² = 49
B - 2A = 49
Now
A + B - B + 2A = 115 - 49
A + 2A = 66
3A = 66
A = 66/3
A = 22
By using 2
B - 2(22) = 49
B - 44 = 49
B = 49 + 44
B = 93
A - B = 22 - 93 = -71