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Question
I am studying for a test and am having trouble working a review question. the original problem is √(2x+7)-√(x+3)=1. I have worked it a couple of times and I am not able to find the correct answer. Thanks in advance
Hi Tom,
Well, follow through my algebra and see if you understand each step.
sqrt(2x + 7) = 1 + sqrt(x+3)
2x + 7 = x + 3 + 2sqrt(x + 3) + 1
x + 3 = 2sqrt(x + 3)
(x + 3)^2 = 4(x + 3)
x + 3 = 0 OR x + 3 = 4
so x = -3, 1
Now, for square root problems, you always have to plug your answers back in since things can go wrong. In this case, they both work, so the answer is
x = -3 ,1
I hope this helps,
Robi
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Answers by Expert:
Robi Bhattacharjee
Expertise
I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.
Experience
I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).
Organizations
I am in the San Diego Math Circle
Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.
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