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Expert: Robi Bhattacharjee - 9/16/2008


Question
square root (x^2-t^2) = 2t-x
If x and t are positive numbers that satisfy the equation above, what is the value of x/t?

Answer
Hello Emily

For this problem, you have to play around with it a bit.

So sqrt(x^2 - t^20) = (2t - x)

This means that

x^2 - t^2 = (2t - x)^2

So x^2 - t^2 = 4t^2 - 4xt + x^2

5t^2 = 4xt

5/4 = xt / t^2

5/4 = x/t

so 5/4. Basically, you just square both sides and cancel the x^2.


I hope this helped,
Robi

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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).

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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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