Question

(2+√3)^4+(2-√3)^4=x+y√3 so find y​

Answer 1

Finding the value of y:

Step-by-step explanation:

$\ Given \ that:\\\\\ (2+\sqrt3)^4 + \ (2-\sqrt3)^4 \ = x+ y \sqrt3 \\\\\ find \ the \ value \ of \ y:\\\\\ Solve:\\\\(2+\sqrt3)^4 + \ (2-\sqrt3)^4 \ = x+ y \sqrt3 \\\\((2+\sqrt3)^2)^2 + ((2-\sqrt3)^2)^2 \ = x + y \sqrt3 \\\\((2)^2+(\sqrt3)^2+2.2.\sqrt3))^2+((2)^2+(\sqrt3)^2-2.2.\sqrt3))^2 \ = x \ + \ y \sqrt3$$\\(4+3+4\sqrt3)^2+(4+3+4\sqrt3)^2 \ = x \ + \ y \sqrt3\\\\(7+4\sqrt3)^2+(7+4\sqrt3)^2 \ = x \ + \ y \sqrt3\\\\((7)^2+(4\sqrt3)^2+2.7.4\sqrt3)+((7)^2+(4\sqrt3)^2-2.7.4\sqrt3)\ = x \ + \ y \sqrt3\\\\ (49+48+56\sqrt3)+(49+48-56\sqrt3)\ = x \ + \ y \sqrt3\\\\ (97+56\sqrt3+97-56\sqrt3)\ = x \ + \ y \sqrt3\\\\(97+97)\ = x \ + \ y \sqrt3\\\\(194)\ = x \ + \ y \sqrt3\\\\\ (194 + 0\sqrt3)\ = x \ + \ y \sqrt3\\\\compairing \ the \ above \ value \\\\ x \ = \ 194 \ \ and \ y \ = \ 0$

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