Lemma 2 Ifa and y are distinct rational numbers, then there is a rational number z which lies strictly between x and y. Hint: If a

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Lemma 2 and lemma 3 needed to be solved correctly in 30 minutes and get the thumbs up please show me neat and clean solution needed
Lemma 1 If x and y are positive real numbers, then
1
2
xy x² + y2¹
2
with equality if and only if x = y.
Lemma 2 If x and y are distinct rational numbers, then there is a rational number z which lies strictly
between x and y.
Hint: If <y are any real numbers, what number is guaranteed to lie between them?
Lemma 3 The equation 7x5 +4x³+13=0 has no solution with x € Z.
Transcribed Image Text:Lemma 1 If x and y are positive real numbers, then 1 2 xy x² + y2¹ 2 with equality if and only if x = y. Lemma 2 If x and y are distinct rational numbers, then there is a rational number z which lies strictly between x and y. Hint: If <y are any real numbers, what number is guaranteed to lie between them? Lemma 3 The equation 7x5 +4x³+13=0 has no solution with x € Z.
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