Advertisements
Advertisements
Question
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Advertisements
Solution
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (a + b + c)^2 = 16 + 2(10)` [`∵ a^2 + b^2 + c^2 = 16` and ab + bc + ca = 10]
`=> (a + b + c)^2 = 16 + 20`
`=> (a + b + c) = sqrt36`
`=> a + b + c = +-6`
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
4y2 – 4y + 1
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
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 a + b = 10 and ab = 21, find the value of a3 + b3
Evaluate of the following:
1043 + 963
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
Find the following product:
(3x + 2y) (9x2 − 6xy + 4y2)
Find the following product:
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 a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If a + b + c = 0, then write the value of \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\]
If a1/3 + b1/3 + c1/3 = 0, then
The product (x2−1) (x4 + x2 + 1) is equal to
Expand the following:
(x - 5) (x - 4)
Find the squares of the following:
3p - 4q2
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
