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
Advertisements
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: `( 2x - 1/x )( 3x + 2/x )`
Expand : `( 3a + 2/b )( 2a - 3/b )`
If x + 2y + 3z = 0 and x3 + 4y3 + 9z3 = 18xyz ; evaluate :
`[( x + 2y )^2]/(xy) + [(2y + 3z)^2]/(yz) + [(3z + x)^2]/(zx)`
If x > 0 and `x^2 + 1/[9x^2] = 25/36, "Find" x^3 + 1/[27x^3]`
If 2( x2 + 1 ) = 5x, find :
(i) `x - 1/x`
(ii) `x^3 - 1/x^3`
If a2 + b2 = 34 and ab = 12; find : 7(a - b)2 - 2(a + b)2
If x2 + `x^(1/2)`= 7 and x ≠ 0; find the value of:
7x3 + 8x − `7/x^3 - 8/x`
If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.
Find the value of 'a': 4x2 + ax + 9 = (2x - 3)2
