Advertisements
Advertisements
Question
Write in the expanded form: `(x/y + y/z + z/x)^2`
Advertisements
Solution
We have
`(x/y + y/z + z/x)^2 = (x/y)^2 + (y/z)^2 + (z/x)^2 + 2. x/y.y/z + 2 y/z. z/x + 2. z/x. x/y`
`[∵ (a + b + c)^2 = a^2 + b^2 + 2ab + c^2 + 3bc + 2ca]`
`∴ (x/y + y/z + z/x)^2 = x^2/y^2 + y^2/z^2 + z^2/x^2 + 2 x/z + 2 y/x + 2 z/y`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Write in the expand form: `(2x - y + z)^2`
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Simplify of the following:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
Evaluate:
483 − 303 − 183
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Expand the following:
(a + 3b)2
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
Expand the following:
(–x + 2y – 3z)2
