Question

if x=3-2√2 find the value of x3-1/x3

Answer 1

take cube both side in equation
x=3-2✓2
x^3=(3-3✓2)^3

x^3=9+9×2-3×3×3✓2(3-3✓2)

x^3=27-81✓2+161
x^3=188-81✓2

put the value of x^3 in equation
x^3-1/x^3

188-81✓2-1/188-81✓2

(188-81✓2)^2-1/188-81✓2.
further you could also open it but it's enough now.

2-short cut method to find the value of x^3-1/x^3


first you need to find value of x from first equation (x=3-3√2)
put value of ✓2=1.4

so x=3-2(1.4)
x=3-2.8=0.2
put value of x=0.2 in equation second(x^3-1/x^3)
=(0.2)^3-1/(0.2)^3
=0.008 -1/0.008
=((0.008)^2-1)/0.008
=(0.000064-1)/0.008
=0.99/0.008=123.75.
now further u can check the option.
and which ans. giving value near to 123 ,tiick the answer and move to the next question.
second method you can do without the use of pen and paper !☺ hope you getting it!