Question

if x= 9-4 root 5 then find the value of x 2 +1/x 2

Answer 1

x=(9-4root5)
1/x=1/(9-4root5)
here rationalising factor = (9+4root5)
multiplying numerator and denominator with rationalising factor we get,
1×(9+4root5)/(9-4root5)×(9+4root5)
(9+4root5)/(9²-(4root5)²)
=(9-4root5)/81-80
=(9+4root5)/1
therefore 1/x = (9=4root5)
x+1/x = (9+4root5)
x+1/x=9-4root5+9=4root5....................eq.1
=9+9
=18
squaring both sides,
(x+1/x)²=18²
(x+1/x)²=x²+(1/x)²+2×x×1/x
x²+1/x²+2=324
x²+1/x²=324-2=322

Answer 2

ANSWER

=> 1/X = 9 minus 4 root 5

=> (x+1/x)^2 = x^2 (1/x)^2+2×x×1/x

=> x^2+(1/x)^2+2=324

=> x^2+1/x=324 minus 2

=>322