Advertisements
Advertisements
प्रश्न
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Advertisements
उत्तर
We have,
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
`= [x^2 + y^2 + z^2 + 2xy + 2yz + 2zx] + [x^2 + y^2/4 + z^2/9 + 2x . y/2 + 2 (zx)/3 + (yz)/3] - [x^2/4 + y^2/9 + z^2/10 + (xy)/3 + (xz)/4 + (yz)/6]`
`= x^2 + y^2 + z^2 + x^2 + y^2/4 + z^2/9 - x^2/4 - y^2/9 - z^2/16 + 2xy + 2x . y/2 - (xy)/3 + 2yz + (yz)/3 - (yz)/6 + 2zx + (2zx)/3 - (xz)/4`
`= (8x^2 - x^2)/4 + (36y^2 + 9y^2 - 4y^2)/36 + (144z^2 + 16z^2 - 9z^2)/144 + (6xy + 3xy - xy)/3 + (13yz)/6 + (29xz)/12`
`= (7x^2)/4 + (41y^2)/36 + (151z^2)/144 + (8xy)/3 + (13yz)/6 + (29zx)/12`
`∴ (x + y + z)^2 + (x + y/2 + z/3)^2 - (x/2 + y/3 + z/4)^2`
`= (7x^2)/4 + (41y^2)/36 + (151Z^2)/144 + (8xy)/3 + (13yz)/6 + (29zx)/12`
APPEARS IN
संबंधित प्रश्न
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Write the following cube in expanded form:
`[x-2/3y]^3`
Evaluate the following using identities:
(0.98)2
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
if `x^2 + 1/x^2 = 79` Find the value of `x + 1/x`
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Write in the expanded form: (-2x + 3y + 2z)2
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
If a + b = 10 and ab = 21, find the value of a3 + b3
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: (6 − 5xy) (6 + 5xy)
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Simplify:
(2x + y)(4x2 - 2xy + y2)
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
