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
Expand the following, using suitable identity:
(x + 2y + 4z)2
Factorise the following:
27y3 + 125z3
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Evaluate the following using identities:
117 x 83
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Evaluate of the following:
`(10.4)^3`
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
Use identities to evaluate : (998)2
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Expand the following:
`(4 - 1/(3x))^3`
