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
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Simplify (a + b + c)2 + (a - b + c)2
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Evaluate of the following:
(9.9)3
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If a + b = 8 and ab = 6, find the value of a3 + b3
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
The product (x2−1) (x4 + x2 + 1) is equal to
Use identities to evaluate : (97)2
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Evaluate the following without multiplying:
(95)2
Which one of the following is a polynomial?
Expand the following:
(3a – 5b – c)2
