if x^2+1/x^2=51,find x-1/x. 2). x^3-1/x^3
Answers
Answered by
3
Answer:
+/-7
+/- 364
Step-by-step explanation:
let x-1/x = t
t^2 = x^2 - 2 + 1/x^2 = 51 - 2 = 49
t = +/- 7 = x-1/x
x^3 - 1/x^3 = (x-1/x)(x^2+1+1/x^2)=+/-7 * 52 = +/- 364
Answered by
4
it is given that, x² + 1/x² = 51
we have to find (1.) x - 1/x and (2.) x³ - 1/x³
now, x² + 1/x² = 51
or, (x - 1/x)² + 2x.1/x = 51
[ as we know, (a - b)² + 2ab = a² + b² ]
or, (x - 1/x)² + 2 = 51
or, (x - 1/x)² = 49 = (7)²
taking square root both sides,
or, (x - 1/x) = ± 7
hence, (x - 1/x) = 7 or -7
now, x³ - 1/x³ = (x - 1/x)³ + 3x.1/x(x - 1/x)
[ as we know, a³ - b³ = (a - b)³ + 3ab(a - b)]
= (x - 1/x)³ + 3(x - 1/x)
= (7)³ + 3(7)
= 343 + 21
= 364
similarly putting (x - 1/x) = -7
then, x³ - 1/x³ = (-7)³ + 3(-7)
= -364
hence, (x³ - 1/x³) = 364 or -364
Similar questions
Science,
5 months ago
English,
5 months ago
History,
5 months ago
Social Sciences,
10 months ago
Math,
10 months ago
Social Sciences,
1 year ago