How many real roots?
Question How many real roots does the following equation have: x^5 + 7*x^3 + 3*x + 2 =…
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Let n, m be an element of Z+ and a,b be elements of Z. Suppose that a=b(modn) and a =b(modm) and that (n,m)=1. Prove that a=b(mod nm)
Answer Z+ means positive integers. Proof. (a – b) is divisible by n. (a – b) = pn…
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What is the minimum value of X + 1/X=?
Answer Let’s assume further that x is positive real. We start with a simple fact that ANY squares…
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Which is greater: 2^3,000,000 or 3^2,000,000 ???
Answer The Answer : 3^(2,000,000) Here’s a simple way. 3,000,000 = 3 x 1,000,000 2,000,000 = 2 x…
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Major city tour problem?
Question A tourist wants to visit 3 or more of the 5 major cities in india : Delhi,Mumbai,Chennai,Kolkata,…
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Compute the following for the given Z(n)?
Question Write your answer in the from [a] where 0 is greater or = to a, and a…
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Complete the following pattern and what do you think this pattern really is? 6, 24, 60, 120, 210, …?
Answer 6 = 1 x 2 x 3 24 = 2 x 3 x 4 60 = 3…
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Can someone PROVE hero’s (or Heron’s) formula?
Answer We use the formula area = (1/2)bc.sin(A) The formula above can be “proven” easily by definition that…
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How do you solve the question 8 8’s = 1000?
Answer It’s classic one and usually people only know “one way” to solve it. There are two ways…
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For how many whole numbers between 0 and 1000 does the sum of the digits equal 9 ?
Answer Let your whole number be ‘X’. Now, 0 < X < 1000 means that your numbers are…