Advertisements
Advertisements
प्रश्न
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
विकल्प
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
Factorise the following:
27y3 + 125z3
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
Simplify (a + b + c)2 + (a - b + c)2
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Evaluate:
483 − 303 − 183
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If a + b = 7 and ab = 12, find the value of a2 + b2
Find the square of 2a + b.
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
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 :
(x+1) (x−1)
Use the direct method to evaluate :
(3b−1) (3b+1)
Use the direct method to evaluate :
(2a+3) (2a−3)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
