Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
how to find range of x^2 + 2xy + 3y^2 -6x -2y .dont use cauchy schwartz inequality.
Dear Manuj,
make the expression quadratic in x taking y as constant
x^2 + 2xy + 3y^2 -6x -2y = 0
and that will be
x^2 +(2y-6)x+(3y2 -2y) = 0
now the range can be found out by taking discriminant greater than equal to 0
We are all IITians and here to help you in your IIT JEE preparation.
Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar : Click here to download the toolbar..
jitender
thanks for ur efforts but here it is not given tht equation has real roots.it may be possible equation is >0 for all real x and y.so how can we use discriminant >=0???.....plzz ans...
Hi Manuj,
Differentiate the equation though the method of differentiation of implicit functions and put the dy/dx = 0 (at maxima and minima, slope of curve=0 ).
it will give u a equation of form 2x+2y-6=0 ==> x+y= 3 ==> x=3-y
Now substitute x by (3-y) in the equation x2 + 2xy + 3y2 -6x -2y = 0 .
It will give you a quardatic equation in y. Find the roots of the equation and they will be the respective maximas and minimas of the equation.
So the range of this function will be [1/2(-2-root(22)),1/2(root(22)-2)]
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !