Advertisements
Advertisements
प्रश्न
If a1/3 + b1/3 + c1/3 = 0, then
पर्याय
a + b + c = 0
(a + b + c)3 =27abc
a + b + c = 3abc
a3 + b3 + c3 = 0
Advertisements
उत्तर
Given `a^(1/3) +b^(1/3) +c^(1/3) = 0`
Using identity `a^3 +b^3 +c^3 = 3abc` we get
Here `a= a^(1/3) ,b=b^(1/3) , c = c^(1/3) `
`(a^(1/3))^3 + (b^(1/3))^3 +(c^(1/3))^3 = 3 xx a^(1/3) xx b^(1/3) xx c^(1/3)`
`(3sqrta)^3 +(3sqrtb)^3 +(3sqrtc)^3 =3 xx 3sqrta xx 3sqrtb xx3sqrt c`
`a+b+c = 3 xx 3sqrt a xx 3sqrtb xx 3sqrtc`
Taking Cube on both sides we get,
`(a+b+c)^3 = (3xx 3sqrta xx 3sqrtb xx 3sqrtc)^3`
`(a+b+c)^3 = 27abc`
Hence the value of `a^(1/3) +b^(1/3) +c^(1/3) = 0` is `(a+b+c)^3 = 27abc` .
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
95 × 96
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
If a − b = 4 and ab = 21, find the value of a3 −b3
Simplify of the following:
(x+3)3 + (x−3)3
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(xy+4) (xy−4)
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Simplify by using formula :
(2x + 3y) (2x - 3y)
Simplify by using formula :
(x + y - 3) (x + y + 3)
If x + y = 9, xy = 20
find: x2 - y2.
Factorise the following:
9y2 – 66yz + 121z2
