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Question Number 195291 by Matica last updated on 29/Jul/23

i t i s g i v e n a, b, c \in N^{*} a n d a b < c . P r o v e t h a t a + b ⩽ c .

Answered by Frix last updated on 29/Jul/23

c = a b + 1

a + b ⩽ a b + 1

Let a < b

b - a b ⩽ 1 - a

b (1 - a) ⩽ 1 - a

This is always true for a = 1 \land b \in N^{*}

For a > 1 :

1 - a < 0 \Rightarrow b (1 - a) ⩽ 1 - a \Leftrightarrow b ⩾ 1 which is

true because b \in N^{*}

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