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05 Sep 2013, 12:17
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Question Stats:
65% (02:22) correct
35%
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If \(b = a + 4\), for which of the following values of \(x\) is the expression \((x - a)^2 + (x - b)^2\) the smallest?
A. \(a-1\)
B. \(a\)
C. \(a + 2\)
D. \(a + 3\)
E. \(a + 5\)
M19-18
A. \(a-1\)
B. \(a\)
C. \(a + 2\)
D. \(a + 3\)
E. \(a + 5\)
M19-18
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26 Dec 2014, 07:40
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If \(b = a + 4\), for which of the following values of \(x\) is the expression \((x - a)^2 + (x - b)^2\) the smallest?
A. \(a-1\)
B. \(a\)
C. \(a + 2\)
D. \(a + 3\)
E. \(a + 5\)
Given \(b = a + 4\), we can rewrite the expression \((x - a)^2 + (x - b)^2\) as \((x - a)^2 + (x - a - 4)^2\). To find the smallest value, substitute each answer choice for \(x\).
The smallest expression value is attained at \(x = a + 2\): \((x - a)^2 + (x - a - 4)^2\) becomes \((a + 2 - a)^2 + (a + 2 - a - 4)^2 = 8\).
Answer: C
A. \(a-1\)
B. \(a\)
C. \(a + 2\)
D. \(a + 3\)
E. \(a + 5\)
Given \(b = a + 4\), we can rewrite the expression \((x - a)^2 + (x - b)^2\) as \((x - a)^2 + (x - a - 4)^2\). To find the smallest value, substitute each answer choice for \(x\).
The smallest expression value is attained at \(x = a + 2\): \((x - a)^2 + (x - a - 4)^2\) becomes \((a + 2 - a)^2 + (a + 2 - a - 4)^2 = 8\).
Answer: C
05 Sep 2013, 12:39
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lets take a= 0 ; then b=4 and the equation becomes x^2+(x-4)^2. The minimum value of this function occurs when
x^2 = (x-4)^2 as both of these functions are increasing functions.
Solving this we get x=2 it is minimum. for a=0 option c is gives the value of x as 2.
hope it helps!
x^2 = (x-4)^2 as both of these functions are increasing functions.
Solving this we get x=2 it is minimum. for a=0 option c is gives the value of x as 2.
hope it helps!
