No Guessing Allowed

Algebra Level 2

If a + a + a a × a × a = b 3 ⟹ a = 1 b \color{#D61F06}\text { If }\frac{ a+ a + a}{a\times a\times a} = b^3 \implies a =\frac{1}{b}

Among the given options, what could be the possible value of b = ? b =?

3 4 1 7 5

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Chew-Seong Cheong
Feb 17, 2018

a + a + a a × a × a = b 3 3 a a 3 = b 3 Given a = 1 b 3 b 1 b 3 = b 3 3 b 2 = b 3 ⟹ b = 3 \begin{aligned} \frac {a+a+a}{a\times a \times a} & = b^3 \\ \frac {3a}{a^3} &= b^3 & \small \color{#3D99F6} \text{Given }a=\frac 1b \\ \frac {\frac 3b}{\frac 1{b^3}} &=b^3 \\ 3b^2 &=b^3 \\ \implies b &=\boxed{3}\end{aligned}

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Thank you sir.

Hana Wehbi - 3 years, 3 months ago

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