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Question

If x4+1x4=47, then the value of x3+1x3 is ......

A
18
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B
27
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C
14
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D
12
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Solution

The correct option is A 18
Given,
x4+1x4=47
We know,
(x2+1x2)2=(x2)2+(1x2)2+2(x2)(1x2)
=x4+1x4+2
=47+2
=49
=>x2+1x2=7
=>(x+1x)2=x2+1x2+2(x)(1x)
=7+2
=9
=>x+1x=3
We know that,
x3+1x3=(x+1x)(x2+1x2x×1x)
=3(71)
=18
Ans A

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