Question

Prove that
(a)
$(\sqrt{3} + \sqrt{5} ) ^{2}$
(b)
$\frac{1}{ \sqrt{2} } + \sqrt{2}$
are an irrational number.​

Answer 1

Hii

your solution is attached above.........

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Answer 2

Answer:

Note that 2–√+3–√ is a solution to the equation:

x4−10x2+1=0

To find this polynomial, note that if x=2–√+3–√, then:

x2=5+26–√

and:

x4=49+206–√.

You need −10x2's to get rid of the 206–√ in x4, and x4−10x2=−1, so you get:

x4−10x2+1=0.