If x = √3 + 2√2 and y = √3 - 2√2 then the value of x4 + y4 + 6 x2y2 is

(A)    584

(B)     682

(C)     798

(D)     245

Asked by gpnkumar0 | 29th Mar, 2017, 05:22: PM

Expert Answer:

begin mathsize 16px style straight x equals square root of 3 plus 2 square root of 2 space space and space straight y equals square root of 3 minus 2 square root of 2
rightwards double arrow straight x squared equals open parentheses square root of 3 plus 2 square root of 2 close parentheses squared space space and space straight y squared equals open parentheses square root of 3 minus 2 square root of 2 close parentheses squared space
rightwards double arrow straight x squared equals 3 plus 8 plus 4 square root of 6 space space and space straight y squared equals 3 plus 8 minus 4 square root of 6 space
rightwards double arrow straight x squared equals 11 plus 4 square root of 6 space space and space straight y squared equals 11 minus 4 square root of 6 space
Now comma
straight x to the power of 4 plus straight y to the power of 4 plus 6 straight x squared straight y squared
equals left parenthesis straight x right parenthesis squared plus left parenthesis straight y right parenthesis squared plus 6 straight x squared straight y squared
equals left parenthesis 11 plus 4 square root of 6 right parenthesis squared plus left parenthesis 11 minus 4 square root of 6 right parenthesis squared plus 6 left parenthesis 11 plus 4 square root of 6 right parenthesis left parenthesis 11 minus 4 square root of 6 right parenthesis
equals 121 plus 88 square root of 6 plus 96 plus 121 minus 88 square root of 6 plus 96 plus 6 left square bracket 121 minus 96 right square bracket
equals 242 plus 192 plus 150
equals 584 end style

Answered by Rebecca Fernandes | 29th Mar, 2017, 05:51: PM