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Let a and b be the roots of the quadratic equation 2x^2 - 8x + 7 = 0. Find 1/(2*a) +1/(2*b)

 Jun 4, 2016
 #1
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Solve for x:
2 x^2-8 x+7=0

 

Divide both sides by 2:
x^2-4 x+7/2=0

 

Subtract 7/2 from both sides:
x^2-4 x=-7/2

 

Add 4 to both sides:
x^2-4 x+4=1/2

 

Write the left hand side as a square:
(x-2)^2=1/2

 

Take the square root of both sides:
x-2=1/sqrt(2) or x-2=-1/sqrt(2)

 

Add 2 to both sides:
x=2+1/sqrt(2) or x-2=-1/sqrt(2)

 

Add 2 to both sides:
Answer: |  x=2+1/sqrt(2)      or          x=2-1/sqrt(2)

 

Youn can finish the 2nd part.

 Jun 4, 2016
 #2
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Let α and β be the 2 roots of the equation ax2+bx+c

α+β=ba

αβ=ca

12α+12β

=α+β2αβ

=822(72)

=47

 Jun 5, 2016

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