Question

If a^1/2= b^1/3 = c^1/4. And abc = 8, what is the value of a?

A. 21/3
B. 41/3
C. 31/3
D. 21/4
E. 21/2

Answer 1

Answer:

B. 4$^{^{\frac{1}{3}}}$

Step-by-step explanation:

Given,

    $a^{\frac{1}{2}}=b^{\frac{1}{3}}=c^{\frac{1}{4}}$

Now, let $k = a^{\frac{1}{2}}=b^{\frac{1}{3}}=c^{\frac{1}{4}}$

Consider $k = a^{\frac{1}{2}}$  ⇒ $a = k^2$

Consider $k = b^{\frac{1}{3}}$  ⇒ $b = k^3$

Consider $k=c^{\frac{1}{4}}$  ⇒ $c=k^4$

Now, given that

               $abc = 8$

         ⇒   $k^{^2}k^{^3}k^{^4}=8$          

         ⇒   $k^{^{2+3+4}}=8$

         ⇒   $k^9=2^3$

         ⇒   $(k^3)^{^3}=2^3$

         ⇒   $k^3=2$

         ⇒   $k = \sqrt[3]{2}$

It was stated that a = k²

∴ a = (∛2)² = ∛2² = ∛4 = 4$^{^{\frac{1}{3}}}$ (Option B)

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Answer 2

The Answer is Option B.