+972 Let a and b be the solutions to 7x^2 + x - 5 = -3x^2 - 9x - 4. Compute (a - 4)/(b - 4) + (b - 4)/(a - 4).
+1950 First, let's simplify the equation we are given. We get
10x2+10x−1ab=−1/102ab=−2/10=−1/5
Now, take a + b = -1
Squaring both sides, we get
a2+2ab+b2=1a2−1/5+b2=1a2+b2=1+1/5=6/5
(a−4)/(b−4)+(b−4)/(a−4)=[(a−4)2+(b−4)2]]′[(a−4)(b−4)]=[a2−8a+16+b2−8b+16]/[ab−4(a+b)+16]=[(a2+b2)−8(a+b)+32]/[ab−4(a+b)+16]=[6/5−8(−1)+32][−1/10−4(−1)+16]=[6/5+40]/[20−1/10]=20497/25
The answer is 20497/25
Thanks! :)
