Question

If , find the value of x=7-4√3 then what is x³+1/x³​

Answer 1

Answer:

hey here is your answer ✌

2702

Step-by-step explanation:

X= 7–4√3

X^3 =( 7–4√3)^3

Formula (a-b)^3 = a^3-3a^2b+3ab^2-b^3

= (7)^3 - 3(7)^2*4√3+3*7*(4√3)^2 - (4√3)^3

= 343–3*49*4√3+3*7*4√3*4√3- 64*3√3

= 343–588√3+1008- 192√3

=343+1008–588√3–192√3

=1351–780√3

1351–780√3

1/x = 1/(7–4√3)

7+4√3÷(7–4√3)(7+4√3) Rationalising the denominator

7+4√3/49–48= 7+4√3/1 = 7+4√3

1/X^3 =(7+4√3)^3

(a+b)^3=a^3 +3a^2b +3ab^2+b^3

(7+4√3)^3= 343+588√3+1008+192√3

= 343+1008+588√3+192√3

= 1351+780√3

1351+780√3

Adding 1351–780√3+1351+780√3

= 1351+1351 = 2702

hope it helps you ✌✌✌✌