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Question

If α and β are the roots equations x234x+1=0, then find 4α4β.

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Solution

x234x+1=0
x=b±b24ac2
=34±(34)24×1×12×1
=34±11522
=34±2422=17±122
α=17+122,β=17122
4α±4β=417+22417122
=[(17+122)12]12[(17122)12]12
=(3+22)12(3+22)12
=(2+1)(21)
=2+12+1
=2.

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