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Interview prep / Brainteaser/Logic

Fourth powers from a given sum and product

Question

Two numbers x,yx,y have sum 1010 and product 2020. Compute x4+y4x^4+y^4.

Short answer

2800. First x2+y2=(x+y)2−2xy=60x^2+y^2=(x+y)^2-2xy=60. Then x4+y4=(x2+y2)2−2(xy)2=3600−800=2800x^4+y^4=(x^2+y^2)^2-2(xy)^2=3600-800=2800.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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