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2018 AMC 10AProblem 10P1-10~2 minPrint
Algebraic ManipulationExponents, Logarithms & RadicalsApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

Suppose that real number xx satisfies 49−x2−25−x2=3.\sqrt{49-x^2}-\sqrt{25-x^2}=3. What is the value of 49−x2+25−x2\sqrt{49-x^2}+\sqrt{25-x^2} ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.