Advertisements
Advertisements
Question
If a – b = 3 and ab = 10, find : a3 – b3.
Advertisements
Solution
a − b = 3
⇒ (a − b)3 = (3)3
⇒ a3 − b3 − 3ab (a − b) = 27
⇒ a3 − b3 − 3×10 (3) = 27
⇒ a3 − b3 − 90 = 27
⇒ a3 − b3 = 27 + 90
⇒ a3 − b3 = 117
Alternative Method :
(a − b)3 = a3 − b3 − 3ab (a − b)
⇒ (3)3 = a3 − b3 − 3×10 (3)
⇒ 27 = a3 − b3 − 90
⇒ 27 + 90 = a3 − b3
⇒ 117 = a3 − b3
⇒ a3 − b3 = 117
APPEARS IN
RELATED QUESTIONS
If a – b = 6 and ab = 16, find a2 + b2
If a + b + c = 10 and a2 + b2 + c2 = 38, find : ab + bc + ca
Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.
Find:
`a^3-1/a^3`, if `a -1/a = 4`.
If `2"x"-1/(2"x")=4`, find: `8"x"^3-1/(8"x"^3)`
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
If a2 + b2 = 41 and ab = 4, find : a – b
If a + b + c = 11 and a2 + b2 + c2 = 81, find : ab + bc + ca.
If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.
If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.
