Question

if x=7+4√3 then find the value of (x +1/x)^2​

Answer 1

X=7+4√3

1/X will be equal to 1/7+4√3= 1(7-4√3)/(7+4√3)(7-4√3) .....rationalising the denominator

1/X=7-4√3/49-48=7-4√3

now, (X+1/X)²= (7+4√3+7-4√3)²=(14)²= 196..

hope this helps..

Answer 2

(x+1/x) ^2=x^2+2 x×1/x+(1/x) ^2
put x=7+4√3
=(7+4√3) ^2+2+1/(7+4√3) ^2
=49+4×3+2+1/49+4×3
=49+12+2+1/49+12
=63+1/61
=3843\61+1/61
=3844/61
=63.01