prove that 7-6√5 is irriational number
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Let 7-6√5 be rational no. Of the form p/q where p is not = 0.
P/q= 7-6√5
7-p/q = -6√5
LHS
( diff b/w rational no is rational)
-6(7-p/q) = √5
LHS(product of rational is rational)
But on RHS it is √5 which is an irrational no.
Product of rational no cant be equal to irrational.
Therefore, 7-6√5 is an irrational no
P/q= 7-6√5
7-p/q = -6√5
LHS
( diff b/w rational no is rational)
-6(7-p/q) = √5
LHS(product of rational is rational)
But on RHS it is √5 which is an irrational no.
Product of rational no cant be equal to irrational.
Therefore, 7-6√5 is an irrational no
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