Question

Please solve this.....


And if you don't know how it will solve than please don't wrote other answer...

Thx❤​

Answer 1

Answer:

108+76root2 is the answer

Answer 2

Given:-

→x-1/x= 3+2√2

To find:-

→Value of x³-1/x³

Solution:-

We know that:-

=>(a-b)³=a³-b³-3ab(a-b)

We shall use the above identity to find the answer.

=>(x-1/x)³ = (x³-1/x³)-3×x×1/x(x-1/x)

=>(x-1/x)³ = (x³-1/x³)-3(x-1/x)

=>x³-1/x³ = (x-1/x)³+3(x-1/x)

=>x³-1/x³ = (3+2√2)³+3(3+2√2)

=>x³-1/x³ = 3+2√2[ (3+2√2)²+3 ]

=>x³-1/x³ = 3+2√2(9+8+3+12√2)

=>x³-1/x³ = (3+2√2)(20+12√2)

=>x³-1/x³ = 3(20+12√2)+2√2(20+12√2)

=>x³-1/x³ = 60+36√2+40√2+48

=>x³-1/x³ = 108+76√2

Thus,value of (x³-1/x³) is (108+76√2).

Some Extra Identities:-

•(a+b)³ = a³+b³+3ab(a+b)

•(a-b)³ = a³-b³-3ab(a-b)

•(a³+b³) = (a+b)(a²+b²-ab)

•(a³-b³) = (a-b)(a²+b²+ab)