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QOTD # 20 If a and b are the two solutions of the equation x
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12 Sep 2016, 02:25
12 Sep 2016, 02:25
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Question Stats:
94% (00:58) correct
5% (01:25) wrong based on 127 sessions
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If a and b are the two solutions of the equation x² – 5x + 4 = 0, what is the value of \((\frac{1 + a}{a})(\frac{1 + b}{b})\) ?
Give your answer as a fraction.
Give your answer as a fraction.
Show: :: OA
\(\frac{5}{2}\)
Practice Questions
Question: 20
Page: 182
Question: 20
Page: 182
Re: QOTD # 20 If a and b are the two solutions of the equation x
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12 Sep 2016, 02:30
12 Sep 2016, 02:30
2
Expert Reply
Explanation
Factoring the quadratic equation x² – 5x + 4 = 0, you get (x – 1)(x – 4) = 0, so the two solutions are either a = 1 and b = 4 or a = 4 and b = 1. Note that a and b are interchangeable in the expression \(\frac{1 + a}{a} * \frac{1 + b}{b}\) so the value of the expression will be the same regardless of the choices of a and b. Thus, substituting we do have
\(\frac{1 + 1}{1} * \frac{1 + 4}{4} = 2* \frac{5}{4} = \frac{5}{2}\)
Factoring the quadratic equation x² – 5x + 4 = 0, you get (x – 1)(x – 4) = 0, so the two solutions are either a = 1 and b = 4 or a = 4 and b = 1. Note that a and b are interchangeable in the expression \(\frac{1 + a}{a} * \frac{1 + b}{b}\) so the value of the expression will be the same regardless of the choices of a and b. Thus, substituting we do have
\(\frac{1 + 1}{1} * \frac{1 + 4}{4} = 2* \frac{5}{4} = \frac{5}{2}\)
Re: QOTD # 20 If a and b are the two solutions of the equation x
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20 May 2021, 09:18
20 May 2021, 09:18
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