Prove that x+√5 is not a rational number
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Ya x+√5 is not a rational number because its a number not determine in p/q face and q is equal to not zero...
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i hope its help u so mark me as the BRAINLIST..__:-)
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Let x+√5 be a rational no.
That is, we can find coprime a and b (b≠0) such that x+√5 =a/b
√5 = a/b - x ... Eq 1
√5 = a-bx/b (taking LCM of ... Eq 1)
We know that √5 is irrational and a-bx/b is integer/integer = rational
Therefore, the equation formed will be..
Irrational = rational (which is not possible)
Therefore, our supposition is wrong x+√5 is not rational. It is irrational.
Hence, Proved!!
That is, we can find coprime a and b (b≠0) such that x+√5 =a/b
√5 = a/b - x ... Eq 1
√5 = a-bx/b (taking LCM of ... Eq 1)
We know that √5 is irrational and a-bx/b is integer/integer = rational
Therefore, the equation formed will be..
Irrational = rational (which is not possible)
Therefore, our supposition is wrong x+√5 is not rational. It is irrational.
Hence, Proved!!
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