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(a-b) = 1, (b-c) = 2 and (c-a) = 3 then the value of (a3 +b3 +c3 -3abc)/(a+b+c) is
- a)5
- b)6
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
(a-b) = 1, (b-c) = 2 and (c-a) = 3 then the value of (a3 +b3 +c3 -3abc...
a3 + b3 + c3 - 3 a b c = ( a + b + c ) ( a2 + b2 + c2 - bc - ab - ac ) .
(a3 +b3 +c3 -3abc)/(a+b+c)
= 1/2[(a-b) 2+(b-c)2 +(c-a)2]
= ½(1+4+9)
= 14/2 = 7
(a3 +b3 +c3 -3abc)/(a+b+c)
= 1/2[(a-b) 2+(b-c)2 +(c-a)2]
= ½(1+4+9)
= 14/2 = 7
Most Upvoted Answer
(a-b) = 1, (b-c) = 2 and (c-a) = 3 then the value of (a3 +b3 +c3 -3abc...
Add all 3 equations given
a-b+b-c+c-a = 1+2+3
0 = 6
a-b+b-c+c-a = 1+2+3
0 = 6
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(a-b) = 1, (b-c) = 2 and (c-a) = 3 then the value of (a3 +b3 +c3 -3abc...
Given: (a-b) = 1, (b-c) = 2 and (c-a) = 3
To find: (a3 b3 c3 -3abc)/(a b c)
Solution:
1. Find the values of a, b and c:
Adding all three equations, we get:
(a-b) + (b-c) + (c-a) = 1 + 2 + 3
=> -2a + 2b - 2c = 6
=> a - b + c = -3
Adding the first two equations, we get:
(a-b) + (b-c) = 1 + 2
=> a - c = 3
Substituting the value of (a-c) in the above equation, we get:
b = 0
Substituting the values of b and a-c in the equation (a-c) = 3, we get:
a = 6 and c = 3
2. Substitute the values of a, b and c in the given expression:
(a3 b3 c3 -3abc)/(a b c) = [(63)3 + 03 + 33 - 3(6)(0)(3)]/(6 * 0 * 3)
= [(216 + 27) - 0]/0
= 243/0
As 0 is not a valid denominator, the given expression is undefined.
Therefore, the answer is not possible.
To find: (a3 b3 c3 -3abc)/(a b c)
Solution:
1. Find the values of a, b and c:
Adding all three equations, we get:
(a-b) + (b-c) + (c-a) = 1 + 2 + 3
=> -2a + 2b - 2c = 6
=> a - b + c = -3
Adding the first two equations, we get:
(a-b) + (b-c) = 1 + 2
=> a - c = 3
Substituting the value of (a-c) in the above equation, we get:
b = 0
Substituting the values of b and a-c in the equation (a-c) = 3, we get:
a = 6 and c = 3
2. Substitute the values of a, b and c in the given expression:
(a3 b3 c3 -3abc)/(a b c) = [(63)3 + 03 + 33 - 3(6)(0)(3)]/(6 * 0 * 3)
= [(216 + 27) - 0]/0
= 243/0
As 0 is not a valid denominator, the given expression is undefined.
Therefore, the answer is not possible.
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