help@askiitians.com

1800-150-456-789

Discuss with colleagues and IITians> The least value of the expression x^2 + 2...

question mark

The least value of the expression x^2 + 2y^2 + 2xy +4y +7 is

muktesh singh , 10 Years ago

Grade 11

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$f(x,y) = x^{2}+2y^{2}+2xy+4y+7$
$f(x,y) = x^{2}+y^{2}+2xy+y^{2}+4y+7$
$f(x,y) = x^{2}+y^{2}+2xy+y^{2}+4y+4 + 3$
$f(x,y) = (x+y)^{2}+(y+2)^{2}+ 3$
x, y belong to R.
Minimum will of the square of any real number is zero.
Minima of f(x, y) will be at
$x = 2, y = -2$
$[f(x,y)]_{min} = (2+(-2))^{2}+(-2+2)^{2}+ 3$
$[f(x,y)]_{min} = 3$

Provide a better Answer & Earn Cool Goodies

Enter text here...

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

question mark

Are core branches(Mechanical) in Top 3 NIT worth it ?

Discuss with colleagues and IITians

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

My rank in JEE Advanced 2022 is 1871. Should I go for IIT Guwahati ECE or IIT Kanpur Mechanical and try for a branch change to CS or Electrical Engineering? Is changing your branch very difficult?

Discuss with colleagues and IITians

1 Answer Available

Last Activity: 2 Year ago(s)

question mark

What awaits me after jee and do you think it's worth it?

Discuss with colleagues and IITians

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Can i sacrifice board exams for jee mains as board exams are no where valueable as cuet and other will be seen for admission

Discuss with colleagues and IITians

0 Answer Available

Last Activity: 2 Year ago(s)

question mark

Is a student studying in IGCSE syllabus eligible for taking IOQP or IOQJS?

Discuss with colleagues and IITians

0 Answer Available

Last Activity: 2 Year ago(s)

View all Questions