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Olympiad question

1) I want a correct explanation please: A semi-circle is drawn outwardly on chord AB of the circle with center O and unit radius. The perpendicular from O to AB, meets the semi-circle on AB at C. Determine the measure of angle( AOB ) and length AB so that OC has maximum length.

2) Find the number of numbers <= \(10^{8}\) which are neither perfect squares,nor perfect cubes, nor perfect fifth powers.

Note by Snehdeep Arora
3 years, 11 months ago

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angle90 Abhimanyu Manu · 3 years, 11 months ago

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V easy. It's an elementary problem of inclusion n exclusion. First u take out the no of squares ie 10000 n similarily cubes n fifth powers n subtract the no of 6th, 15th ,10th powers and add the 30th power nos. I hope u got it.. if u want my written solution I ll mail it to u.. but the answer is 10^8 - 10474. Priyanshi Somani · 3 years, 11 months ago

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The answer to the first is a bit obvious but I like the second one. What is the relation between squares? How can we find the difference between two squared numbers without squaring them? I hope its clear. Addismiraph Abebe · 3 years, 11 months ago

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jmo questions........... answer to 1 is 90 degree . Did you complete rest of the questions? Kumar Ashutosh · 3 years, 11 months ago

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