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Question

If 2(x2+1)=5x, find x31x3.
  1. ±173
  2. ±638
  3. ±138
  4. ±38

A
±173
B
±138
C
±638
D
±38
Solution
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2(x2+1)=5x
=>x2+1x=52
=>x+1x=52
Squaring both sides,
=>x2+1x2+2(x)+(1x)=254
=>x2+1x2=2542
=>x2+1x2=174
Now,
(x1x2)2=x2+1x22(x)+(1x)
=1742
=94
=>x1x=±94
=±32
Now,
x31x3=(x1x)[(x2+1x2+(x)(1x)]
=(±32)(174+1)
=(±32)(214)
=±638

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