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Answers
Explanation:
Given :-
a+b = a×b = a÷b
To find :-
Find the values of a and b ?
Solution :-
Given that
a+b = a×b = a÷b
On taking a+b = a×b
=> a = ab-b
=> a = b(a-1)
=> b = a/(a-1) -------(1)
On taking a×b = a÷b
=> ab = a/b
=> b =1/b
=> b² = 1
=> b = ±√1
=> b = ±1
Therefore, b = 1 and -1
Now,
Case -1:-
If b = 1 then equation (1) becomes
=> 1 = a/(a-1)
=> (a-1) = a
=> a-a = 1
=> 0 = 1
It is impossible .
so , b ≠ 1
Case -2:-
If b = -1 then equation (1) becomes
=> -1 = a/(a-1)
=> -1×(a-1) = a
=> -(a-1) = a
=> -a+1 = a
=> 1 = a+a
=> a+a = 1
=> 2a = 1
=> a = 1/2
Therefore, a = 1/2
Therefore, a = 1/2 and b = -1
Answer:-
The values of a and b are 1/2 and -1 respectively.
Check:-
If a = 1/2 and b = -1 then
a+b = (1/2)+(-1)
=> a+b = (1/2)-1
=> a+b = (1-2)/2
=> a-b = -1/2
and
a×b = (1/2)×-1 = -1/2
a/b = (1/2)/-1 = -1/2
a+b = a×b = a÷b = -1/2
a+b = a×b = a÷b is true for a = 1/2 and
b = -1
Verified the given relations in the given problem.