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Algebra Level 2

Find the least value of s s for the below equation.

1 s − 1 s + 1 = 1 72 \large \dfrac{1}{s}-\dfrac{1}{s+1}=\dfrac{1}{72}


The answer is -9.

Anish Harsha by Anish Harsha , 20, India

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2 solutions

Akshat Sharda
Nov 28, 2015

1 s − 1 s + 1 = 1 72 ⇒ 1 s ( s + 1 ) = 1 72 s 2 + s − 72 = 0 ⇒ ( s + 9 ) ( s − 8 ) = 0 Least value of x = − 9 \frac{1}{s}-\frac{1} {s+1}=\frac{1}{72} \Rightarrow \frac{1}{s(s+1)}=\frac{1}{72} \\ s^2+s-72=0 \Rightarrow (s+9)(s-8)=0 \\ \text{Least value of x}=\boxed{-9}

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. .
May 16, 2021

1 s − 1 s + 1 = 1 72 → s + 1 s ( s + 1 ) − s s ( s + 1 ) = 1 72 → s + 1 − s s ( s + 1 ) = 1 72 → 1 s ( s + 1 ) = 1 72 → s ( s + 1 ) = 72 → s 2 + s − 72 = 0 → ( s + 9 ) ( s − 8 ) = 0 → s = − 9 or s = 8 ∴ \displaystyle \frac { 1 } { s } - \frac { 1 } { s + 1 } = \frac { 1 } { 72 } \rightarrow \frac { s + 1 } { s ( s + 1 ) } - \frac { s } { s ( s + 1 ) } = \frac { 1 } { 72 } \rightarrow \frac { s + 1 - s } { s ( s + 1 ) } = \frac { 1 } { 72 } \rightarrow \frac { 1 } { s ( s + 1 ) } = \frac { 1 } { 72 } \rightarrow s ( s + 1 ) = 72 \rightarrow s ^ { 2 } + s - 72 = 0 \rightarrow ( s + 9 ) ( s - 8 ) = 0 \rightarrow s = -9 \text { or } s = 8 \therefore the least value of s s is − 9 \boxed { -9 } .

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