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Question's in the image.

I will rt(5) to mean the root(5), which is the squareroot(5).

As I read the question, the 1st term in brackets on the left becomes 5*rt(5).

The next term turns into 8*rt(5)/5.

The last term turns into -8/5.

The multiplier is 2/(rt(5)+2).

On the right, we have (2/5)(m+nrt(5)).

The equation is then This gives (5*rt(5) + 8*rt(5)/5 - 8/5)(2/(rt(5)+2)) = (2/5)(m+n*rt(5)).

Multiplying by (rt(5)+2))/2 gives 5*rt(5) + 8*rt(5)/5 - 8/5 = ((rt(5)+2)/5)(m+n*rt(5)).

Multiplying by 5 gives 25*rt(5) + 8*rt(5) - 8 = (rt(5)+2)(m+n*rt(5)).

Combining the 1st two terms on the left gives 33*rt(5) - 8 = (rt(5)+2)(m+n*rt(5)).

Multiplying both sides by rt(5)-2 gives 165 - 8*rt(5) - 66*rt(5) + 16 = m+n*rt(5).

Combining terms on the left gives 181 - 75*rt(5).

From here, is can be seen that m = 181 and n = -66.

Algebra

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