Prove that 1/2-root 5⬇️ is an irrational no ..
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Answered by
12
Hey!
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Let , 1/2 - √5 be a rational number
Then,
1/2-√5 = p/q
2-√5 = q/p
√5 = 2-q/p
√5 = 2 - p/q
√5 = 2q/p
2p/q is a rational number, then √5 should be rational too.
.
But, this contradicts the fact that √5 is an irrational number, so our supposition is totally wrong and 1/2-√5 is an irrational number.
_________________
Hope it helps...!!!
_________________
Let , 1/2 - √5 be a rational number
Then,
1/2-√5 = p/q
2-√5 = q/p
√5 = 2-q/p
√5 = 2 - p/q
√5 = 2q/p
2p/q is a rational number, then √5 should be rational too.
.
But, this contradicts the fact that √5 is an irrational number, so our supposition is totally wrong and 1/2-√5 is an irrational number.
_________________
Hope it helps...!!!
mysticd:
it is wrong , plz , check again
Answered by
19
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