Advertisements
Advertisements
Question
The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares
Solution
Given difference between two positive numbers is 4 and difference between their cubes is 316.
Let the positive numbers be a and b
a - b = 4 .....(1)
a3 - b3 = 316 .....(2)
ab = 21 .....(3)
Squaring(eq 1) both sides, we get
(a - b)2 = 16
a2 + b2 - 2ab = 16
a2 + b2 = 2 × 21 + 16
a2 + b2 = 42 + 16
a2 + b2 = 58
Sum of their squares is 58.
APPEARS IN
RELATED QUESTIONS
Expand : ( x + 8 ) ( x + 10 )
Expand : ( 5a - 3b + c )2
If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.
If x+ y - z = 4 and x2 + y2 + z2 = 30, then find the value of xy - yz - zx.
In the expansion of (2x2 - 8) (x - 4)2; find the value of coefficient of x2
If 2( x2 + 1 ) = 5x, find :
(i) `x - 1/x`
(ii) `x^3 - 1/x^3`
If a2 + b2 = 34 and ab = 12; find : 3(a + b)2 + 5(a - b)2
Find the value of 'a': 9x2 + (7a - 5)x + 25 = (3x + 5)2
If x = `1/[ 5 - x ] "and x ≠ 5 find "x^3 + 1/x^3`
If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`
