.“Integers does not satisfy the associative property with respect to subtraction”. Justifyit.
Answers
Answer:
9
Step-by-step explanation:
Required Numbers are (11,12)
\begin{gathered}Or\\ < /p > < p > (\frac{-12}{23},\frac{11}{23})\end{gathered}Or</p><p>(23−12,2311)
Step-by-step explanation:
\begin{gathered} Let\:x \:and \:(x+1) \:are\\ < /p > < p > two \: consecutive\: numbers \end{gathered}Letxand(x+1)are</p><p>twoconsecutivenumbers
Sum\:of\: the\: reciprocals=\frac{23}{132}Sumofthereciprocals=13223
\implies \frac{1}{x}+\frac{1}{x+1}=\frac{23}{132}⟹x1+x+11=13223
\implies \frac{x+1+x}{x(x+1)}=\frac{23}{132}⟹x(x+1)x+1+x=13223
\implies \frac{2x+1}{x^{2}+x}=\frac{23}{132}⟹x2+x2x+1=13223
\implies 132(2x+1)=23(x^{2}+x)⟹132(2x+1)=23(x2+x)
\implies 264x+132=23x^{2}+23x⟹264x+132=23x2+23x
\implies 0=-264x-132+23x^{2}+23x⟹0=−264x−132+23x2+23x
\implies 23x^{2}-241x-132=0⟹23x2−241x−132=0
/* Splitting the middle term, we get
\implies 23x^{2}-263x+12x-132=0⟹23x2−263x+12x−132=0
\implies 23x(x-11)+12(x-11)=0⟹23x(x−11)+12(x−11)=0
\implies (x-11)(23x+12)=0⟹(x−11)(23x+12)=0
\implies x-11=0\:Or\:23x+12=0⟹x−11=0Or23x+12=0
\implies x=11\:Or\:23x=12⟹x=11Or23x=12
\implies x=11\:Or\:x =\frac{-12}{23}⟹x=11Orx=23−12
Therefore,
Case 1:
If x = 11, x+1 = 11+1 = 12
case 2:
\begin{gathered}If \:x =\frac{-12}{23}\\ < /p > < p > x+1=\frac{-12}{23}+1\\=\frac{-12+23}{23}\\=\frac{11}{23}\end{gathered}Ifx=23−12</p><p>x+1=23−12+1=23−12+23=2311
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