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02 Jun 2022, 23:27
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C
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If (a + b) = 4, and ab = 7/4, what is the value of a^2 – b^2?
A. -12
B. 12
C. Either A or B
D. 16
E. None
A. -12
B. 12
C. Either A or B
D. 16
E. None
04 Jun 2022, 11:02
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It is given that (a + b) = 4 and ab = \(\frac{7}{4}\).
The value of \(a^2\) – \( b^2\) is to be calculated. Using standard algebraic identities, \(a^2\) – \(b^2\) = (a + b) (a – b)
Since the value of (a + b) is already given, we need the value of (a – b) to calculate the value of the given expression.
Using standard algebraic identities, \((a – b) ^2\) = \((a + b)^2\) – 4ab.
Substituting the values, \((a -b)^2\) = \((4)^2\) – 4 * \(\frac{7}{4}\) = 16 – 7 = 9
Therefore, (a – b) = 3 or (a – b) = -3
If (a – b) = 3, the value of \(a^2\) – \(b^2\) = 4 * 3 = 12.
If (a – b) = -3, the value of \(a^2\) – \(b^2\) = 4 * -3 = -12.
Therefore, the value of \(a^2\) – \(b^2\) could be 12 or -12.
The correct answer option is C.
The value of \(a^2\) – \( b^2\) is to be calculated. Using standard algebraic identities, \(a^2\) – \(b^2\) = (a + b) (a – b)
Since the value of (a + b) is already given, we need the value of (a – b) to calculate the value of the given expression.
Using standard algebraic identities, \((a – b) ^2\) = \((a + b)^2\) – 4ab.
Substituting the values, \((a -b)^2\) = \((4)^2\) – 4 * \(\frac{7}{4}\) = 16 – 7 = 9
Therefore, (a – b) = 3 or (a – b) = -3
If (a – b) = 3, the value of \(a^2\) – \(b^2\) = 4 * 3 = 12.
If (a – b) = -3, the value of \(a^2\) – \(b^2\) = 4 * -3 = -12.
Therefore, the value of \(a^2\) – \(b^2\) could be 12 or -12.
The correct answer option is C.
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