0

Guest

Courses New

IF (x-y)f(x+y)-(x+y)f(x-y)=4xy(x+y)(x-y)for all x,y find f(x).

IF (x-y)f(x+y)-(x+y)f(x-y)=4xy(x+y)(x-y)for all x,y find f(x).

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
243-2144_capture.PNG
mycroft holmes
272 Points
5 years ago
Let a = (x+y), b = (x-y) then x = \frac{a+b}{2}, y = \frac{a-b}{2}
 
Then the equation can be written as 
 b f(a) – a f(b) = ab (a2-b2). 
Setting b = 1, we get f(a) – a f(1) = a3-a 
Let f(1) = k, then f(a) = a3+(k-1)a
 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Top Engineering Colleges in India

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More