Question

find all triples (a,b,c) with a,b, and c are positive integer such that (1 + 1/a)(1 + 1/b)(1 + 1/c) = 2

Answer 1

Solve for:
Let's solve for a.
(1+
1
a
)(1+
1
b
)(1+
1
c
)=2
Step 1: Multiply both sides by abc.
abc+ab+ac+bc+a+b+c+1=2abc
Step 2: Add -2abc to both sides.
abc+ab+ac+bc+a+b+c+1+−2abc=2abc+−2abc
−abc+ab+ac+bc+a+b+c+1=0
Step 3: Add -bc to both sides.
−abc+ab+ac+bc+a+b+c+1+−bc=0+−bc
−abc+ab+ac+a+b+c+1=−bc
Step 4: Add -b to both sides.
−abc+ab+ac+a+b+c+1+−b=−bc+−b
−abc+ab+ac+a+c+1=−bc−b
Step 5: Add -c to both sides.
−abc+ab+ac+a+c+1+−c=−bc−b+−c
−abc+ab+ac+a+1=−bc−b−c
Step 6: Add -1 to both sides.
−abc+ab+ac+a+1+−1=−bc−b−c+−1
−abc+ab+ac+a=−bc−b−c−1
Step 7: Factor out variable a.
a(−bc+b+c+1)=−bc−b−c−1
Step 8: Divide both sides by -bc+b+c+1.
a(−bc+b+c+1)
−bc+b+c+1
=
−bc−b−c−1
−bc+b+c+1
a=
−bc−b−c−1
−bc+b+c+1
Answer:
a=
−bc−b−c−1
−bc+b+c+1

Answer 2

@rational
i need help :D

Answer 3

\[(1 + \frac{ 1 }{a })(1 + \frac{ 1 }{b })(1 + \frac{ 1 }{c }) = 2\]

Answer 4

\[(\frac{ a+1 }{ a })(\frac{ b+1 }{ b })(\frac{ c+1 }{ c }) = 2\]

Answer 5

(a + 1)(b + 1)(c + 1) = 2abc

Answer 6

Solve for:
Let's solve for a.
(a+1)(b+1)(c+1)=2abc
Step 1: Add -2abc to both sides.
abc+ab+ac+bc+a+b+c+1+−2abc=2abc+−2abc
−abc+ab+ac+bc+a+b+c+1=0
Step 2: Add -1 to both sides.
−abc+ab+ac+bc+a+b+c+1+−1=0+−1
−abc+ab+ac+bc+a+b+c=−1
Step 3: Add -c to both sides.
−abc+ab+ac+bc+a+b+c+−c=−1+−c
−abc+ab+ac+bc+a+b=−c−1
Step 4: Add -b to both sides.
−abc+ab+ac+bc+a+b+−b=−c−1+−b
−abc+ab+ac+bc+a=−b−c−1
Step 5: Add -bc to both sides.
−abc+ab+ac+bc+a+−bc=−b−c−1+−bc
−abc+ab+ac+a=−bc−b−c−1
Step 6: Factor out variable a.
a(−bc+b+c+1)=−bc−b−c−1
Step 7: Divide both sides by -bc+b+c+1.
a(−bc+b+c+1)
−bc+b+c+1
=
−bc−b−c−1
−bc+b+c+1
a=
−bc−b−c−1
−bc+b+c+1
Answer:
a=
−bc−b−c−1
−bc+b+c+1