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Question

If a−1a=3, find a2+3a+1a2−3a.

A
20
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B
12
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C
32
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D
17
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Solution

The correct option is A 20
Given,
a1a=3
Squaring both sides,
=>(a1a)2=32
=>a2+1a22(a)(1a)=9
=>a2+1a2=9+2
=>a2+1a2=11
now,
a2+3a+1a23a
=a2+1a2+3a+3a
=a2+1a2+3(a1a)
=11+3(3)
=11+9
=20

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