Math, asked by shahbhavita12, 2 months ago


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


HarshithScamander: Please mark my answer Brainliest
shahbhavita12: Ok thank you
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Answers

Answered by HarshithScamander
3

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)

Hope it helps!!! Please mark Brainliest!!!

Answered by studier123
0

The Answer is Option B.

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