If a^b=b^c=ab, then b+c=
Solve by class 9 method
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HELLO DEAR,
GIVEN:- a^b = b^c = ab = k(say)
so, a^b = k , b^c = k , ab = k
also, a = k^{1/b} , b = k^{1/c} , ab = k
now, ab = k^{1/b} * k^{1/c}
ab = k^{1/b + 1/c}
ab = k^{(c + b)/bc}
[as , ab = k ]
k = k^{(b + c)/bc}
1 = (b + c)/bc
b + c = bc
hence, b + c = bc
I HOPE IT'S HELP YOU DEAR,
THANKS
GIVEN:- a^b = b^c = ab = k(say)
so, a^b = k , b^c = k , ab = k
also, a = k^{1/b} , b = k^{1/c} , ab = k
now, ab = k^{1/b} * k^{1/c}
ab = k^{1/b + 1/c}
ab = k^{(c + b)/bc}
[as , ab = k ]
k = k^{(b + c)/bc}
1 = (b + c)/bc
b + c = bc
hence, b + c = bc
I HOPE IT'S HELP YOU DEAR,
THANKS
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