Advertisements
Advertisements
Question
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
Advertisements
Solution
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (9)^2 = a^2 + b^2 + c^2 + 2(23)`
`=> 81 = a^2 + b^2 + c^2 + 46` [∵ a + b + c = 9 and (ab + bc + ca = 23)]
`=> a^2 + b^2 + c^2 = 81 - 46`
`=> a^2 + b^2 + c^2 = 35`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(3 – 2x) (3 + 2x)
Factorise the following using appropriate identity:
4y2 – 4y + 1
Factorise the following:
27y3 + 125z3
Write in the expanded form:
`(a + 2b + c)^2`
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
Evaluate of the following:
(9.9)3
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
The product (x2−1) (x4 + x2 + 1) is equal to
Find the square of : 3a + 7b
Find the square of `(3a)/(2b) - (2b)/(3a)`.
Use identities to evaluate : (101)2
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate :
(4+5x) (4−5x)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate the following without multiplying:
(999)2
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
