Answers

The Brainliest Answer!
2016-04-02T04:59:07+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Solutions 

We expand the given expression to obtain

(x² + 6x + 9) + 2(y² − 4y + 4) + 4(x² − 14x + 49) + (y² + 8y + 16) 

We expand further to obtain  

x² + 6x + 9 + 2y² − 4y + 4+ 4x² − 14x + 49 + (y² + 8y + 16 

We simplify to obtain 5x²− 50x + 3y² + 229

We remove a common factor of 5 from the first two terms

5(x²− 10x) + 3y² + 229

and then complete the square to obtain 

5(x²− 10x + 52 − 5² ) + 3y² + 229 

This gives

5(x − 5)² − 125 + 3y² + 229 or 5(x − 5)² + 3y² + 104

Since y ² ≥ 0 for all real numbers y, then the minimum value of 3y² + 24 is 24. Since the minimum value of (x−3)²+4(x−7)² is 80 and the minimum value of 2(y−2)²+(y+4)² is 24, then the minimum value of

(x − 3)² + 2(y − 2)² + 4(x − 7)²+ (y + 4)² is 80 + 24 = 104. 

Answer: (E)
1 5 1