Advertisements
Advertisements
प्रश्न
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
Advertisements
उत्तर
a + 2b + c = 0 ...(i)
⇒ (a + 2b) + c = 0
⇒ (a + 2b)3 + c3 + 3(a + 2b) c(a + 2b + c) = 0
⇒ a3 + 8b2 + 6ab (a + 2b) + c3 + 0 = 0
⇒ a3 + 8b3 + c3 + 6ab (a + 2b) = 0 ....(2)
Using (1), we get a + 2b = -c
From (2),
a3 + 8b3 + 6ab (-c) = 0
⇒ a3 + 8b3 + c3 = 6abc.
APPEARS IN
संबंधित प्रश्न
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
If `( a + 1/a )^2 = 3 "and a ≠ 0; then show:" a^3 + 1/a^3 = 0`.
Use property to evaluate : 93 - 53 - 43
If 4x2 + y2 = a and xy = b, find the value of 2x + y.
If 2x - 3y = 10 and xy = 16; find the value of 8x3 - 27y3.
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`
If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`
Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2
(p + q)(p2 – pq + q2) is equal to _____________
