Advertisements
Advertisements
Question
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Solution
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
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
If \[x - \frac{1}{x} = 7\] ,find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
(7p4 + q) (49p8 − 7p4q + q2)
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If a1/3 + b1/3 + c1/3 = 0, then
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
Use the direct method to evaluate the following products :
(5a + 16) (3a – 7)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Expand the following:
(x - 3y - 2z)2
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
Expand the following:
(4a – b + 2c)2
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
