Prove that 7-`sqrt3` is irrational.
Let `7-sqrt3` is rational number
∴ `7-sqrt3=p/q` (p, q are integers, q ≠ 0)
∴ `7 -p/q=sqrt3`
Here p,q are integers.
∴ `(7q-p)/q` is also integer.
∴ LHS =`sqrt3` is also integer but this sqrt3 is contradiction that is irrational so our assumption is wrong that `7-sqrt3` is rational
∴ `7-sqrt3` is irrational proved.
Let `7-sqrt3` is rational
we know sum or difference of two rationals is also rational.
∴ `7-7-sqrt3 = sqrt3 = `
but this is contradiction that `sqrt3` is irrational
`:.7-sqrt3` is irrational proved.
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