+0  
 
0
12
1
avatar+1688 

Let $a$ and $b$ be the roots of the quadratic equation $2x^2 - 7x + 2 = -x^2 + 4x + 9.$ Find $\frac{1}{a+7}+\frac{1}{b+7}.$

 Mar 8, 2024
 #1
avatar+129659 
+1

Simplify as

 

3x^2  - 11x - 7 =  0

 

Product of  roots    ab  =  -7/3

 

 

Sum of roots  = a + b  = 11/3        

 

 

1/ (a + 7)  +  1/ (b + 7)  =     [ a + b + 14 ] /  [ ab + 7 (a+b) + 49 ]   =

 

[ 11/3 + 14 ]  / [ -7/3 + 7(11/3) + 49 ] =

 

[ 53/3] / [ 70/3 + 49]  =

 

[53/11] / [  217/3]  =

 

[53/3][ 3/217]   =

 

53 / 217

 

cool cool cool

 Mar 8, 2024

5 Online Users

avatar
avatar
avatar
avatar