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A.) Prove that the ratio of two rational numbers must be rational.
b.) Prove that if [tex]\sqrt{d}[/tex] is irrational, and b and c are rational numbers such that,[tex]b+c\sqrt{d} =0[/tex] then we must have b=c=0

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smcamiddle

Answer:

v — Prove that (ax + b)/(cx + d) is irrational if and only if ad = bc. ... If b = 0, we have (ax + b)/(cx + d) = 0 is rational; if c = 0, since ... nonzero integers m, n ∈ Z. Then we have ... Proof. We prove by induction. When n = 1, both sides are 1/2 hence the ... So there are less than (k + 1)(2k + 1)k+1 (actually muc

Step-by-step explanation:

c — Prove that (ax + b)/(cx + d) is irrational if and only if ad = bc. ... If b = 0, we have (ax + b)/(cx + d) = 0 is rational; if c = 0, since ... nonzero integers m, n ∈ Z. Then we have ... Proof. We prove by induction. When n = 1, both sides are 1/2 hence the ... So there are less than (k + 1)(2k + 1)k+1 (actually muc

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