Algebra Warmups

Algebra Warmups: Level 3 Challenges


What is the value of

1%? \large \sqrt{1\text{\%}}\, ?

100001+100003+100005++1999991+3+5+7++99999=? \frac{100001+100003+100005+\cdots+199999}{1+3+5+7+\cdots+99999} = \, ?

Over all real numbers xx, find the minimum value of (x+6)2+25+(x6)2+121 \sqrt{(x+6)^2+25} + \sqrt{(x-6)^2+121} .

(x+3)(x+4)(x+6)(x+7)=1120 \large (x+3)(x+4)(x+6)(x+7) = 1120

Find the sum of all reals xx satisfying the equation above.

2×3=?\large \sqrt{-2}\times\sqrt{-3}=\, ?

In this problem, the square root is a function from the complex numbers to the complex numbers.


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