Q. 7

Using (√7 + √3)(√7 — √3) = 4 and the fact that (√7 + √3) is irrational prove that √7 — √3 is irrational.

Answer :

Given ( + )() = 4 and ( + ) is irrational.


(multiplying numerator and denominator by )


=


(we know that (a – b) × (a + b) = (a2 – b2))


= =


Here, it is given that is irrational and we know that 4 is rational.


Therefore,


We know that rational divided by irrational is always irrational.


So, is irrational.


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