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TTT Questions (Distribution)
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If a^2-b^2=101 and a and b are nonnegative integers, find a+b. (Hint: consider prime factorization of 101) *
If a+b=36 and a*b=4, find 1/a+1/b?(Hint: Consider making 1/a+1/b to 1 fraction) *
How many numbers x are there such that 1<=x<=1000 and x^x is a perfect square?(Hint: Consider parity of exponent)
What is the probability that a randomly chosen divisor of 4! is a perfect square? (Hint: Find prime factorizaiton)
What is the sum of the reciprocals of the roots of x^3+7x^2+14x+28 (Hint: consider Vieta's)
If x+y=17 and x^2+y^2=269, what is xy? (Hint: Consider (x+y)^2)
Find all the solutions to x^3+3x^2-16x-48
If x^2+y^2=5 and x+y=3, what is x^4+y^4?
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