Assuming that √7 is a rational number prove that 4-3√7 is an irrational number
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Let us assume that 4-3√7 is rational number
4-3√7=a/b. {where a and b are the integers}
-3√7=a-4b/b
=>√7=a-4b/-3b
As a/b is rational
so a-4b/-3b is also rational
Here we assumed that √7 is rational number.
But this contradicts the fact that √7 is irrational so our assumption is wrong
Therefore, 4-3√7 is irrational number.
4-3√7=a/b. {where a and b are the integers}
-3√7=a-4b/b
=>√7=a-4b/-3b
As a/b is rational
so a-4b/-3b is also rational
Here we assumed that √7 is rational number.
But this contradicts the fact that √7 is irrational so our assumption is wrong
Therefore, 4-3√7 is irrational number.
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