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If a2 = a + c,where a.c > 0. Which of the following must be true ? a >
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20 Mar 2023, 05:37
20 Mar 2023, 05:37
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If \(a^2 = a + c\),where \(ac > 0\). Which of the following must be true ?
Indicate all that apply
a > 0
a < c
0 < a < 1
a > 1
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Indicate all that apply
a > 0
a < c
0 < a < 1
a > 1
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Re: If a2 = a + c,where a.c > 0. Which of the following must be true ? a >
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30 Mar 2023, 03:50
30 Mar 2023, 03:50
1
We are given that a² = a + c, where ac > 0. We need to determine which of the following statements must be true.
To begin, let's simplify the given equation:
a² - a - c = 0
We can solve this quadratic equation using the quadratic formula:
a = [1 ± sqrt(1 + 4c)] / 2
Since ac > 0, we know that either both a and c are positive or both are negative.
Now, let's consider each statement:
a > 0: This statement must be true, since the solutions to the quadratic formula are both positive.
a < c: This statement may or may not be true, depending on the value of c. If c is negative, then a < c. But if c is positive, then a > c.
0 < a < 1: This statement may or may not be true, depending on the value of c. If c is less than 3/4, then both solutions to the quadratic formula are between 0 and 1. But if c is greater than 3/4, then one solution is greater than 1 and the other is less than 0.
a > 1: This statement may or may not be true, depending on the value of c. If c is greater than 3, then both solutions to the quadratic formula are greater than 1. But if c is less than 3, then one solution is greater than 1 and the other is negative.
Therefore, the only statement that must be true is a > 0. The other statements may or may not be true, depending on the value of c.
Answer: a > 0
To begin, let's simplify the given equation:
a² - a - c = 0
We can solve this quadratic equation using the quadratic formula:
a = [1 ± sqrt(1 + 4c)] / 2
Since ac > 0, we know that either both a and c are positive or both are negative.
Now, let's consider each statement:
a > 0: This statement must be true, since the solutions to the quadratic formula are both positive.
a < c: This statement may or may not be true, depending on the value of c. If c is negative, then a < c. But if c is positive, then a > c.
0 < a < 1: This statement may or may not be true, depending on the value of c. If c is less than 3/4, then both solutions to the quadratic formula are between 0 and 1. But if c is greater than 3/4, then one solution is greater than 1 and the other is less than 0.
a > 1: This statement may or may not be true, depending on the value of c. If c is greater than 3, then both solutions to the quadratic formula are greater than 1. But if c is less than 3, then one solution is greater than 1 and the other is negative.
Therefore, the only statement that must be true is a > 0. The other statements may or may not be true, depending on the value of c.
Answer: a > 0
Re: If a2 = a + c,where a.c > 0. Which of the following must be true ? a >
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30 Aug 2023, 04:49
30 Aug 2023, 04:49
Can we solve it by substituting the c value in the ac> 0 inequality also?
It gives a clear a value in that case.
It gives a clear a value in that case.
