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
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Factorise the following:
27y3 + 125z3
Evaluate the following using identities:
`(2x+ 1/x)^2`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Find the following product:
Find the following product:
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If a − b = 5 and ab = 12, find the value of a2 + b2
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(2a+3) (2a−3)
Expand the following:
(x - 3y - 2z)2
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Expand the following:
(3a – 5b – c)2
Expand the following:
`(1/x + y/3)^3`
