Advertisements
Advertisements
Question
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Advertisements
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:
95 × 96
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
Evaluate of the following:
1113 − 893
Simplify of the following:
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:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
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 \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
Expand the following:
(m + 8) (m - 7)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
Expand the following:
(3a – 5b – c)2
Expand the following:
(–x + 2y – 3z)2
