Show that 3-√5 is an irrational number.
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Step-by-step explanation:
Let us assume that 3 + √5 is a rational number.
Now,
3 + √5 = (a ÷ b)
[Here a and b are co-prime numbers]
√5 = [(a ÷ b) - 3]
√5 = [(a - 3b) ÷ b]
Here, {(a - 3b) ÷ b} is a rational number.
But we know that √5 is a irrational number.
So, {(a - 3b) ÷ b} is also a irrational number.
So, our assumption is wrong.
3 + √5 is a irrational number.
Hence, proved.
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