prove that 2+√3÷5 is an irrational number, given that √3 is an irrational number.
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Answer:
let us assume that (2+√3)/5 is a rational number
and is equal to p/q where p and q are integrs and q is not equal to 0.
so ,
(2+√3)/5 = p/q
2+√3= 5p/q
√3= 5p/q-2
now p/q is rational so 5p/q-2 is rational but it is given that √3 is irrational .
so we arrive at contradiction
hence (2+√3)/5 is a rational number.
hope it helps you
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