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7. If v2 is irrational number. Prove that 3-27 is also irrational.269 |
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Answer» Lets assume that√7 is rational number.ie√7=p/q.suppose p/q have common factor thenwe divide by the common factor to get√7 =a/b were a and b are co-prime number.that is a and b have no common factor.√7 =a/b co- prime number√7= a/ba=√7bsquaringa²=7b² .......1a² is divisible by 7a=7csubstituting values in 1(7c)²=7b²49c²=7b²7c²=b²b²=7c²b² is divisible by 7that is a and b have atleast one common factor 7. This is contradictory to the fact that a and b have no common factor.This is happen because of our wrong assumption.√7 is irrationalHence an irrational number multiplied by 2 is irrational hence 2√7And a number added or subtracted to rational is irrationalhence 3-2√7 is irrational u |
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