The two missing numbers

EasyProgramming & DSA~3m

An array should hold the integers $1$ through $100$ but two are missing. The remaining 98 numbers sum to 4950, and their squares sum to 333150. What is the larger of the two missing numbers?

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The sum gives $a+b$ ; you need a second equation — the sum of squares gives $a^2+b^2$ .
From $a+b$ and $a^2+b^2$ get $ab=\tfrac{(a+b)^2-(a^2+b^2)}{2}$ , then solve $t^2-(a+b)t+ab=0$ .

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The two missing numbers

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