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If a^2/3=b^2/3 for a ≠ 0 and b ≠ 0, then which of the follow
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31 Jan 2020, 05:45
31 Jan 2020, 05:45
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16% (00:54) correct
83% (01:07) wrong based on 36 sessions
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If \(a^{\frac{2}{3}}=b^{\frac{2}{3}}\) for \(a ≠ 0\) and \(b ≠ 0\), then which of the following statements must be true?
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
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Re: If a^2/3=b^2/3 for a ≠ 0 and b ≠ 0, then which of the follow
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31 Jan 2020, 10:58
31 Jan 2020, 10:58
2
Carcass wrote:
If \(a^{\frac{2}{3}}=b^{\frac{2}{3}}\) for \(a ≠ 0\) and \(b ≠ 0\), then which of the following statements must be true?
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
We have: \(a^{\frac{2}{3}}=b^{\frac{2}{3}}\)
Cubing both sides: \(a^{2}=b^{2}\) ... Option E is correct
Dividing throughout by \(b^2\): \(\frac{a^{2}}{b^{2}} = 1\) ... Option C is correct
Why are options A, B and F incorrect?
We have already obtained: \(a^{2}=b^{2}\)
Taking square root: \(|a|=|b|\)
\(=> a = b\) or \(=> a = -b\)
However, we have to choose the options that MUST be true
(Note: Options A and B may be true)
If either of \(a\) and \(b\) are negative (from above), their square root would become imaginary.Hence, option F is also incorrect
Answer: C and E
Re: If a^2/3=b^2/3 for a ≠ 0 and b ≠ 0, then which of the follow
[#permalink]
24 Apr 2020, 02:04
24 Apr 2020, 02:04
1
Carcass wrote:
If \(a^{\frac{2}{3}}=b^{\frac{2}{3}}\) for \(a ≠ 0\) and \(b ≠ 0\), then which of the following statements must be true?
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
Indicate \(all\) possible values.
\(\square\) \(\frac{a}{b}=1\)
\(\square\) \(\frac{a}{b}=-1\)
\(\square\) \((\frac{a}{b})^2=1\)
\(\square\) \(a=\frac{2}{3}\)
\(\square\) \(a^2=b^2\)
\(\square\) \(\sqrt{a}=\sqrt{b}\)
There are 6 options after the question but only A,B,C,D and E (5 options to answer). Please could you update
