Math, asked by vv798763734, 1 year ago

prove that √2+√5 is irrational​

Answers

Answered by Anonymous
12

Answer:

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Step-by-step explanation:

Use proof by contradiction. Assume that the sum is rationial, that is

2–√+5–√=ab

where a and b are integers with b≠0. Now rewrite this as

5–√=ab−2–√.

Squaring both sides of this equation we obtain

5=a2b2−22–√ab+2.

Now, carefully solve for 2–√ and obtain

2–√=−3b2a+a2b.

This implies that 2–√ is a rational number which is a contradiction. Thus

2–√+5–√

is an irrational number.

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