Math, asked by bindhu78, 1 year ago

find the solution for above question?

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shadowsabers03: Bro., remember this equation. If x^2 + (1/x^2) = n, then x^3 + (1/x^3) = (n + 2)^(1/2) x (n - 1) and x^3 - (1/x^3) = (n - 2)^(1/2) x (n + 1).

bindhu78: me sister

shadowsabers03: Here the answer is (7 + 2)^(1/2) x (7 - 1) = 9^(1/2) x 6 = 3 x 6 = 18.

shadowsabers03: Sister?! I'm boy!

bindhu78: ok

bindhu78: thanks bye

shadowsabers03: Sorry, I didn't see you so I called bro. Take it as sis. Thanks.

Answers

Answered by YagamiLight

x^2+1/x^2=7
add 2 on both sides.
x^2+1/x^2+2=9
(x+1/x)^2=9
x+1/x=√9=3
cubing on both sides.
x^3+1/x^3+3(x)(1/x)(x+1/x)=3^3
substitute the value of x+1/x=3 we obtained above
x^3+1/x^3+3(3)=27
x^3+1/x^3+9=27
x^3+1/x^3=27-9=18

hope it helps

Answered by siddhartharao77

Given x^2 + 1/x^2 = 7

= > x^2 + 1/x^2 + 2 = 9

= > (x + 1/x)^2 = 9.

= > x + 1/x = 3.

Now,

on cubing both sides, we get

= > (x + 1/x)^3 = (3)^3

= > x^3 + 1/x^3 + 3(x + 1/x) = 27

= > x^3 + 1/x^3 + 3(3) = 27

= > x^3 + 1/x^3 + 9 = 27

= > x^3 + 1/x^3 = 18.

Hope this helps!

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