If a^1/2 = b^1/3 = c^1/4. And abc = 8, what is the value of a?
A. 213
B. 413
C. 31/3
D. 214
E. 212
Answers
Answer:
213 is the right answer
Step-by-step explanation:
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Step-by-step explanation:
Answer:
B. 4^{^{\frac{1}{3}}}
3
1
Step-by-step explanation:
Given,
a^{\frac{1}{2}}=b^{\frac{1}{3}}=c^{\frac{1}{4}}a
2
1
=b
3
1
=c
4
1
Now, let \begin{gathered}k = a^{\frac{1}{2}}=b^{\frac{1}{3}}=c^{\frac{1}{4}}\\\end{gathered}
k=a
2
1
=b
3
1
=c
4
1
Consider k = a^{\frac{1}{2}}k=a
2
1
⇒ a = k^2a=k
2
Consider k = b^{\frac{1}{3}}k=b
3
1
⇒ b = k^3b=k
3
Consider k=c^{\frac{1}{4}}k=c
4
1
⇒ c=k^4c=k
4
Now, given that
abc = 8abc=8
⇒ k^{^2}k^{^3}k^{^4}=8k
2
k
3
k
4
=8
⇒ k^{^{2+3+4}}=8k
2+3+4
=8
⇒ k^9=2^3k
9
=2
3
⇒ (k^3)^{^3}=2^3(k
3
)
3
=2
3
⇒ k^3=2k
3
=2
⇒ k = \sqrt[3]{2}k=
3
2
It was stated that a = k²
∴ a = (∛2)² = ∛2² = ∛4 = 4^{^{\frac{1}{3}}}
3
1
(Option B)
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