+0  
 
0
10
1
avatar+400 

Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$

 Feb 12, 2024
 #1
avatar+1622 
+1

x^2 + 7x - 4 = -x^2 + 9x + 6, combine like terms:

2x^2 - 2x - 10 = 0

x^2 - x - 5 = 0

By vieta's, the sum of the roots a + b = -1 * the second term / the leading coefficient = 1.

Thus, a + 3 + b + 3 = a + b + 6 = 7

 Feb 12, 2024

0 Online Users