+1855 If $s$ is a real number, then what is the smallest possible value of $2s^2 - 8s + 19 - 7s^2 - 8s + 20$?
+9675 I assume you meant largest.
Simplifying the expression and completing the square, we have
2s2−8s+19−7s2−8s+20=−5s2−16s+39=−5(s2+165s)+39=−5(s+85)2+5(85)2+39=−5(s+85)2+2595
Note that −5(s+85)2≤0 for any real s. Then the largest possible value is 2595.
There is no smallest value. The expression can be arbitrarily small.
+9675 I assume you meant largest.
Simplifying the expression and completing the square, we have
2s2−8s+19−7s2−8s+20=−5s2−16s+39=−5(s2+165s)+39=−5(s+85)2+5(85)2+39=−5(s+85)2+2595
Note that −5(s+85)2≤0 for any real s. Then the largest possible value is 2595.
There is no smallest value. The expression can be arbitrarily small.
