Question

Find the least value of the expression E=3x^2+5y^2-6x-30y+50

Answer 1

@mukushla @RadEn @zepdrix

Answer 2

make 2 complete squares...1 in terms of x another in terms of y

Answer 3

E=3x^2+5y^2-6x-30y+50

3 (x^2 - 2x + 1) + 5 ( y^2-6y + 9) + 50 - 3 -45

Answer 4

3 (x-1)^2 + 5(y-3)^2 + 2 =E

Answer 5

Then ......?

Answer 6

well minimum is 2 :) right??

Answer 7

Yup./..u r ryt ? but how ?

Answer 8

yeah, minimum at poit (1,3), it is 2

Answer 9

\[ (x-1)^2 \ge0\]\[(y-3)^2 \ge 0\]so\[3 (x-1)^2 + 5(y-3)^2 + 2 \ge 0+0+2=2\]notice that 2 squares are independent of each other

Answer 10

Errr.......Thxxx//..

Answer 11

welcome :) tnx raden for medal man :)

Answer 12

Nice solution!