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06 Aug 2009, 02:30
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I solved this exam yesterday. I solved all of the problems. Got the right answers. I liked some of the problems so much that I wanted you to see these. I will post each in its own topic.
if one of the roots of the equation \(x^2+4x-7=0\) is \(a\), then what is the result of the multiplication below?
\((a-1).(a+1).(a+3).(a+5)=?\)
a)12 b)14 c)15 d)18 e)20
if one of the roots of the equation \(x^2+4x-7=0\) is \(a\), then what is the result of the multiplication below?
\((a-1).(a+1).(a+3).(a+5)=?\)
a)12 b)14 c)15 d)18 e)20
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06 Aug 2009, 06:30
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The answer is in this spoiler.
\(x^2+4x-7= x^2+4x+4-11=(x+2)^2-11^=0\)
Then
\((x+2)^2=11\)
this makes
\((a+2)^2=11\)(since a is a root of this equation)
Say \(b=(a+2)\)
Then the equation below becomes :
\((b-3).(b-1).(b+1).(b+3)=(b^2-9).(b^2-1)\) since \((a+2)^2=11\) this makes
\(b^2=11\)
So
\((b^2-9).(b^2-1)=(11-9).(11-1)=20\) Answer is E
Then
\((x+2)^2=11\)
this makes
\((a+2)^2=11\)(since a is a root of this equation)
Say \(b=(a+2)\)
Then the equation below becomes :
\((b-3).(b-1).(b+1).(b+3)=(b^2-9).(b^2-1)\) since \((a+2)^2=11\) this makes
\(b^2=11\)
So
\((b^2-9).(b^2-1)=(11-9).(11-1)=20\) Answer is E
Another question:
What is the equal of \(sqrt{5-sqrt{21}}\)
Answer is
What is the equal of \(sqrt{5-sqrt{21}}\)
Answer is
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