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
Use suitable identity to find the following product:
(x + 8) (x – 10)
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Evaluate following using identities:
991 ☓ 1009
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Evaluate of the following:
463+343
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Expand the following:
(2p - 3q)2
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Evaluate the following without multiplying:
(103)2
Evaluate the following without multiplying:
(1005)2
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
The coefficient of x in the expansion of (x + 3)3 is ______.
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
