Advertisements
Advertisements
प्रश्न
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Advertisements
उत्तर
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (0)^2 = 16 + 2(ab + bc + ca)` `[∵ a + b + c = and a^2 + b^2 + c^2 = 16] `
=> 2(ab + bc + ca) = -16
=> ab + bc + ca = -8
APPEARS IN
संबंधित प्रश्न
Evaluate the following using suitable identity:
(998)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Evaluate of the following:
1113 − 893
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
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 = 6 and ab = 20, find the value of a3 − b3
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If a + b = 7 and ab = 12, find the value of a2 + b2
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
Use identities to evaluate : (97)2
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Expand the following:
(x - 3y - 2z)2
If x + y = 1 and xy = -12; find:
x - y
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
