Advertisements
Advertisements
Question
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
Options
35
58
127
none of these
Solution
We have to find `a^2 + b^2 + c^2`
Given `a+b + c = 9,ab+bc +ca = 23`
Using identity `(a+b+c)^2 = a^2 + b^2 +c^2+2ab + 2bc + 2ca` we get,
`(9)^2 = a^2 +b^2 + c^2+ 2 (ab + bc + ca)`
` 9 xx 9 = a^2 + b^2 + c^2 +2 xx 23`
`81 = a^2 + b^2 + c^2+46`
By transposing +46 to left hand side we get,
`81 - 46 = a^2 +b^2 +c^2`
` 35 = a^2 +b^2 +c^2`
Hence the value of `a^2 +b^2 +c^2` is 35.
APPEARS IN
RELATED QUESTIONS
Factorise the following:
27y3 + 125z3
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Prove that a2 + b2 + c2 − ab − bc − ca is always non-negative for all values of a, b and c
Evaluate of the following:
(9.9)3
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If \[x^4 + \frac{1}{x^4} = 194,\] find \[x^3 + \frac{1}{x^3}, x^2 + \frac{1}{x^2}\] and \[x + \frac{1}{x}\]
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
If a + b = 6 and ab = 20, find the value of a3 − b3
If a − b = −8 and ab = −12, then a3 − b3 =
If a2 + b2 + c2 − ab − bc − ca =0, then
Evalute : `((2x)/7 - (7y)/4)^2`
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Which one of the following is a polynomial?
The value of 2492 – 2482 is ______.
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
