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If a, b and c are positive integers, then find the product of (a + b) (b + c) (c + a).
- a)> 8 abc
- b)<8 abc
- c)=8 abc
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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If a, b and c are positive integers, then find the product of (a + b) ...
Put a= l, b = 2 c = 3 and check through options.
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If a, b and c are positive integers, then find the product of (a + b) ...
The expression (a b) represents the greatest common divisor (GCD) of a and b, while (b c) represents the GCD of b and c, and (c a) represents the GCD of c and a. Since a, b, and c are positive integers, their GCDs will also be positive integers.
The product of these three GCDs can be written as (a b) * (b c) * (c a). By the commutative property of multiplication, we can rearrange the terms to get (a * c) * (b * a) * (c * b).
Since multiplication is commutative, we can group the terms together to get (a * b * c) * (a * a) * (b * b) * (c * c).
The expression a * a is equal to a^2, and the expressions b * b and c * c are equal to b^2 and c^2, respectively.
Substituting these values back into the equation, we get (a * b * c) * a^2 * b^2 * c^2.
The product of (a b) (b c) (c a) is therefore equal to (a * b * c) * a^2 * b^2 * c^2.
The product of these three GCDs can be written as (a b) * (b c) * (c a). By the commutative property of multiplication, we can rearrange the terms to get (a * c) * (b * a) * (c * b).
Since multiplication is commutative, we can group the terms together to get (a * b * c) * (a * a) * (b * b) * (c * c).
The expression a * a is equal to a^2, and the expressions b * b and c * c are equal to b^2 and c^2, respectively.
Substituting these values back into the equation, we get (a * b * c) * a^2 * b^2 * c^2.
The product of (a b) (b c) (c a) is therefore equal to (a * b * c) * a^2 * b^2 * c^2.
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If a, b and c are positive integers, then find the product of (a + b) (b + c) (c + a).a)> 8 abcb)<8 abcc)=8 abcd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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