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Math Challenge III Algebra Practice Question 1.25

 
 
ShiJames的头像
Math Challenge III Algebra Practice Question 1.25
ShiJames - 2020年06月7日 Sunday 12:37
 

For question 1.25, I tried solving for a + b + c + d since that would give me log_2(x) + log_2(y). Then, I could combine this value into log_2(xy) and then raise 2 to that power to find xy. However, I do not know how to approach this question. Could someone help me or give me a hint?

 
ProfessorAreteem的头像
Re: Math Challenge III Algebra Practice Question 1.25
ProfessorAreteem - 2020年06月8日 Monday 20:37
 

What you have so far looks good. You already know that $b + d = 1$, so the goal would be to find what $a + c$ is.

Note that $a$ is an integer and, since $x > 2$, you have that $a \geq 1$. Since $|1 - a|+\sqrt{c - 4} = 1$, what can you say about $|1 - a|$? Use these to find the possible values of $a$. Then use those to find possible values of $c$ in each case.

 
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