Advertisements
Advertisements
प्रश्न
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
पर्याय
108
207
669
729
Advertisements
उत्तर
We have to find the value of `a^3 +b^3 +c^3 - 3abc`
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`
Using identity `a^3 +b^3 +c^3 -3abc = (a+b+c)[a^2 + b^2 +c^2 - (ab+bc+ca)]`
`9 xx [35 -23]`
` = 9 xx 12`
` = 108`
The value of `a^3 +b^3 +c^3 -3abc` is 108.
APPEARS IN
संबंधित प्रश्न
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expand form: `(2x - y + z)^2`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
Find the square of : 3a - 4b
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Evaluate the following without multiplying:
(103)2
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Expand the following:
(3a – 5b – c)2
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
