Advertisements
Advertisements
प्रश्न
Write in the expanded form: `(x/y + y/z + z/x)^2`
Advertisements
उत्तर
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
संबंधित प्रश्न
Evaluate the following using identities:
(2x + y) (2x − y)
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
Find the square of `(3a)/(2b) - (2b)/(3a)`.
If a - b = 7 and ab = 18; find a + b.
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
Using suitable identity, evaluate the following:
1033
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
Simplify (2x – 5y)3 – (2x + 5y)3.
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
