Advertisements
Advertisements
प्रश्न
Simplify (a + b + c)2 + (a - b + c)2 + (a + b - c)2
Advertisements
उत्तर
We have
(a + b + c)2 + (a - b + c)2 + (a + b - c)2
`= [a^2 + b^2 + c^2 + 2ab + 2bc + 2ca] + [a^2 + b^2 + c^2 - 2bc - 2ab + 2ca] + [a^2 + b^2 + c^2 - 2ca - 2bc + 2ab]`
`[∵ (x + y + z)^2 = x^2 + y^2 + 2xy + 2yz + 2zx]`
`= 3a^2 + 3b^2 + 3c^2 + 2ab + 2bc + 2ca - 2bc - 2ab + 2ca - 2ca - 2bc + 2ab`
`= 3a^2 + 3b^2 + 3c^2 + 2ab - 2bc + 2ca`
`= 3(a^2 + b^2 + c^2) + 2(ab - bc + ca)`
`∴(a + b + c)^2 + (a - b + c)^2 + (a + b - c)^2 = 3(a^2 + b^2 + c^2) + 2[ab - bc + ca]`
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
(3a – 7b – c)2
Factorise:
27x3 + y3 + z3 – 9xyz
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
Evaluate the following:
(98)3
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
Find the square of : 3a - 4b
Use identities to evaluate : (97)2
If a - b = 7 and ab = 18; find a + b.
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: (5xy − 7) (7xy + 9)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Find the squares of the following:
(2a + 3b - 4c)
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
