Question

Prove that 3-2V5 is an irrational number

Answer 1

We know that ✓5 is an irrational number


we can proof that 3-2✓5 is an irrational by assuming that it is rational

if 3-2✓5 is rational then it can be expressed in the form p/q where p andq are co prime numbers

therefore
3-2✓5=p/q
2✓5=3-p/q
✓5=(3-p/q)/2

here LHS is irrational number but RHS is a rational number

this contradiction rises because we have assume 3-2✓5 a rational number
thus, 3-2✓5 is irrational number
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