Advertisements
Advertisements
प्रश्न
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
पर्याय
1
–1
0
`1/2`
Advertisements
उत्तर
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is 0.
Explanation:
Consider the equation:
`x/y + y/x = -1`
Simplify the above expression as follows:
`(x^2 + y^2)/(xy) = -1`
x2 + y2 = –xy
Now, x3 – y3 = (x – y)(x2 + y2 + xy)
= (x – y)(–xy + xy) ...[Substitute: x2 + y2 = –xy]
= (x – y) × 0
= 0
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(3a – 7b – c)2
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
933 − 1073
If x = −2 and y = 1, by using an identity find the value of the following
If a − b = −8 and ab = −12, then a3 − b3 =
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Use identities to evaluate : (502)2
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
If x + y = 9, xy = 20
find: x2 - y2.
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
The value of 2492 – 2482 is ______.
Expand the following:
`(4 - 1/(3x))^3`
