Question

find minimum value of x^2+y^2+(x+y+1)^2​

Answer 1

ANSWER BY SACHIN

......

EXPLANATION : -

Given:...... SACHIN....

#2x +y = 10#

We can rewrite in terms of #y# as

#y = 10 - 2x#

Now substitute ????

#x^2 + y^2#

#x^2 + (10 -2x)^2#

#x^2 + 100 - 40x + 4x^2#

Call the value of this expression #A#.

#A = 5x^2 - 40x + 100#

We notice that #A# is a parabola that opens upwards. So to find our minimum we can use differentiation.

#A' = 10x - 40#

The minimum will occur when the derivative equals #0#.

#0 = 10x - 40#

#0 = 10(x - 4)#

#x= 4#

Therefore, the minimum value will occur when #y = 2# and #x = 4#. This means the minimum value is #2^2 + 4^2 = 20#

Hopefully this helps!

Answer 2

Step-by-step explanation:

hi I have completed this question