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I was going through a past paper for my exams when I saw this question. I don't recall ever learning it but I saw a video with a similar question. Can anyone help me out here? I know I am supposed to compare the coefficients but how do I know which ones to compare?

Given that z = a+(a+3)sqrt(3) and z^2 = 79 + bsqrt(3), find the value of each integer a and b

The final answer is suppsed to be a=2 and b=20 but I have no idea how to get there.

garymcmascelyn
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1 Answers1

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$$79+b\sqrt3= a^2+3(a+3)^2+2\sqrt3 a(a+3)$$

As $a,b$ are rational

$$79=a^2+3(a+3)^2\implies a=?$$

$$b=2a(a+3)=?$$

lab bhattacharjee
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