Question

prove that 2 √3-7 is irrational, if it is known that √3 is an irrational number ​

Answer 1

Answer:

Let us assume that 2root3-7 is rational. Now since rhs = rational so root 3 should be rational. But this contradicts the fact in reality that root 3 is irrational . So our assumption is wrong and hence 2 root 3-7 is irrational

Answer 2

Answer:

let 2√3-7 be a rational number.....

2√3-7 = a/b.............[ a and b are co-prime nos.]

2√3 = a+7b/b

√3 = a+7b/2b

a and b are integers , so a+7b/2b is rational.

so √3 is rational

but this contradicts the fact that √3 is irrational,

so 2√3-7 is irrational......