Question

if x = 2 square root 3 , find x square + 1 / x square​

Answer 1

hey mate

here is your solution....

Answer:

given:

x=2+√3

so,

1/x=1/(2+√3)

now, rationalising the denominator

1/x=1/(2+√3)*(2-√3)/(2-√3)

1/x=(2-√3)/(2+√3)(2-√3)

1/x=(2-√3)/(2)²-(√3)²

1/x=(2-√3)/(4-3)

1/x=(2-√3)/1

1/x=(2-√3)

thus,

x+1/x=(2+√3)+(2-√3)

x+1/x=4

squaring both sides,

(x+1/x)²=(4)²

x²+1/x²+2.x.1/x=16

x²+1/x²+2=16

x²+1/x²=16-2

x²+1/x²=14 (answer)