Advertisements
Advertisements
प्रश्न
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
विकल्प
35
58
127
none of these
Advertisements
उत्तर
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
संबंधित प्रश्न
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Evaluate the following using identities:
(399)2
Write in the expanded form:
(2a - 3b - c)2
Write in the expanded form: `(x + 2y + 4z)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
If a + b = 8 and ab = 6, find the value of a3 + b3
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Use the direct method to evaluate :
(2a+3) (2a−3)
Find the squares of the following:
9m - 2n
Simplify:
(7a +5b)2 - (7a - 5b)2
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
