Numerical Trinomial

Find two factors (other than 1 and the number itself) whose product is:

612 + 88 + 278


Show/Hide Solution

612 + 88 + 278  = (2 · 3)12 + (23)8 + (33)8
  = 212312 + 224 + 324
= 224 + 212312 + 324
= 224 + 2(212312) + 324 – 212312
= (212)2 + 2(212312) + (312)2 – 212312
= (212 + 312)2 – (2636)2
= (212 + 312 + 2636)(212 + 312 – 2636)
= 582,193 · 488,881 ≈ 2.84623096 x 1011

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