Prove that 2 + √5 is irrational.
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Answered by
3
Answer:
possible, let us assume 2+ √5 is a rational number.
2+ √5 = p/q where p,q∈z,q
=0
2−
p/q =− √5
q
2q−p
=−
√5
⇒−
√5
is a rational number
∵
q
2q−p
is a rational number
But −
√5
is not a rational number.
∴ Our supposition 2+
√5
is a rational number is wrong.
⇒2+
√5
is an irrational number.
Answered by
0
let us assume that 2 + √5 is not an irrational number.
if 2 + √5 is rational then let 2 + √5 = p upon q.
Therefore we get √5 = p upon q - 2.
In this equation left side is an irrational number and right side rational number which is contradictory, so 2 + √5 is not an rational but it is an irrational number.
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