the sum of a positive number and its reciprocal is 15 divided by 4. then find the number
Answers
Answer:
Valueofx=5orx=
5
1
Step-by-step explanation:
Let \: the \:number = xLetthenumber=x
\begin{lgathered}Reciprocal \: of \: the \\ number=\frac{1}{x}\end{lgathered}
Reciprocalofthe
number=
x
1
\begin{lgathered}Sum \: of \: the \: number \\and \: it's reciprocal = \frac{26}{5}\end{lgathered}
Sumofthenumber
andit
′
sreciprocal=
5
26
x +\frac{1}{x} = \frac{26}{5}x+
x
1
=
5
26
\frac{x^{2}+1}{x}=\frac{26}{5}
x
x
2
+1
=
5
26
\implies 5(x^{2}+1)=26x⟹5(x
2
+1)=26x
\implies 5x^{2}-26x+5=0⟹5x
2
−26x+5=0
\implies 5x^{2}-25x-x+5=0⟹5x
2
−25x−x+5=0
\implies 5x(x-5)-(x-5)=0⟹5x(x−5)−(x−5)=0
\implies (x-5)(5x-1)=0⟹(x−5)(5x−1)=0
\implies x-5=0 \:Or\:5x-1=0⟹x−5=0Or5x−1=0
\implies x = 5 \:Or \: x = \frac{1}{5}⟹x=5Orx=
5
1
Therefore,
Value \: of \: x = 5 \:or\: x=\frac{1}{5}Valueofx=5orx=
5
1
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