English, asked by Anonymous, 2 months ago

\frac { 1 } { ( \sqrt { 2 } + 2 \sqrt { 3 } ) ^ { 2 } }


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Answers

Answered by ajaydhayal
1

Answer:

The answer above is completely correct, but it may help the student to see how to reach it:

We seek a square root of 3−2√2. This must have the form a+b√2.

(a+b√2)2=a2+2ab√2+2b2

So

a2+2b2=3

and

2ab=−2⇒ab=−1

These are two simultaneous equations for a and b.

Rearrange the second:

b=−1a

Substitute into the first:

a2+2a2=3

a4+2=3a2

a4−3a2+2=0

Note that this is a quadratic in a2:

(a2)2−3(a2)+2=0

Factorise:

(a2−2)(a2−1)=0

This gives us two possible solutions for a2: 2 and 1, and so the four solutions for a: ±

Explanation:

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Answered by llMisscutieell
5

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