If x^2+y^2=41 and x+y=4
Then find  x+y and x-y
Please help me solve this problem 

Asked by Siddharth | 23rd Jul, 2016, 07:08: PM

Expert Answer:

begin mathsize 16px style straight x squared plus straight y squared equals 41
and space straight x plus straight y equals 4 space left parenthesis given right parenthesis
rightwards double arrow open parentheses straight x plus straight y close parentheses squared equals 16
rightwards double arrow straight x squared plus straight y squared plus 2 xy equals 16
rightwards double arrow 41 plus 2 xy equals 16
rightwards double arrow 2 xy equals negative 25
rightwards double arrow xy equals fraction numerator negative 25 over denominator 2 end fraction
We space know space that comma space
open parentheses straight x minus straight y close parentheses squared equals straight x squared plus straight y squared minus 2 xy
rightwards double arrow open parentheses straight x minus straight y close parentheses squared equals 41 minus 2 left parenthesis fraction numerator negative 25 over denominator 2 end fraction right parenthesis
rightwards double arrow open parentheses straight x minus straight y close parentheses squared equals 41 plus 25
rightwards double arrow open parentheses straight x minus straight y close parentheses squared equals 66
rightwards double arrow straight x minus straight y equals plus-or-minus square root of 66 end style

Answered by Rebecca Fernandes | 24th Jul, 2016, 11:13: AM

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