1) Prove by absurd that ((ln 2)/(ln 3)) is irrational 2) Prove by absurd that (√2)+(√(6 ))≤(√(15))


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Question Number 158945 by LEKOUMA last updated on 10/Nov/21

$1) P r o v e b y a b s u r d t h a t$ $\frac{\ln 2}{\ln 3} i s i r r a t i o n a l$ $2) P r o v e b y a b s u r d t h a t$ $\sqrt{2} + \sqrt{6} ⩽ \sqrt{15}$
	Answered by mr W last updated on 10/Nov/21

	$s a y$ $\sqrt{2} + \sqrt{6} ⩾ \sqrt{15}$ $8 + 4 \sqrt{3} ⩾ 15$ $4 \sqrt{3} ⩾ 7$ $16 \times 3 ⩾ 49$ $48 ⩾ 49 \Rightarrow c o n t r a d i c t i o n!$
	Commented by LEKOUMA last updated on 10/Nov/21

	$T h a n k s$
	Answered by mr W last updated on 10/Nov/21

	$s a y$ $\frac{\ln 2}{\ln 3} = \frac{p}{q}$ $\ln 2^{q} = \ln 3^{p}$ $2^{q} = 3^{p} \Rightarrow e v e n = o d d \Rightarrow c o n t r a d i c t i o n$
	Commented by LEKOUMA last updated on 10/Nov/21

	$T h a n k s$
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