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अगर p=3+1pp=3+\frac{1}{\mathrm{p}}, तो 5pp2+pकामान1\frac{5 \mathrm{p}}{\mathrm{p}^{2}+\mathrm{p का मान }-1} है :

a

1141 \frac{1}{4}

b

1

c

3123 \frac{1}{2}

d

2132 \frac{1}{3}

Answer : Option A
Explanation :

p1p=3\mathrm{p}-\frac{1}{\mathrm{p}}=3 (Given)

अभिव्यक्ति =5pp2+p1=\frac{5 p}{p^{2}+p-1}

=5pp(p+11p)=5(p1p)+1=53+1=54=114=\frac{5 p}{p\left(p+1-\frac{1}{p}\right)}=\frac{5}{\left(p-\frac{1}{p}\right)+1}=\frac{5}{3+1}=\frac{5}{4}=1 \frac{1}{4}

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