Question

solve this problem ​

Answer 1

Step-by-step explanation:

root3+ root2/root3-root2

x=root3+root2/root3-root2×root3+root2/root3+root2

x=(root3+root2)²/(root3)²-(root2)³

x=(root3)²+(root2)²+2×root3×root2/3-2

x=3+2+2root6/1

x=5+2root6

putting the value of x in x⁴+1/x⁴

=(5+2root6)⁴ + (1/5+2root6)⁴

=(5+2root6)⁴+(1/5+2root6×5-2root6/5-2root6)⁴

=(5+2root6)⁴+{5-2root6/(5)²-(2root6)²}⁴

={(5+2root6)²(5+2root6)²}+{(5-2root6)²(5-2root6)²

={(5)²+(2root6)²+2×5×2root6}{(5)²+(2root6)²+2×5×2root6}+{(5)²+(2root6)²-2×5×2root6}{(5)²+(2root6)²-2×5×2root6}

=(25+24+20root6)(25+24+20root6)+(25+24-20root6)(25+24-20root6)

=(49+2root6)(49+2root6)+(49-2root6)(49-2root6)

=(2401+98root6+98root6+24)+(2401-98root6-98root6+24)

=2425+196root6+2425-196root6

=4850