Advertisements
Advertisements
प्रश्न
If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.
उत्तर
`x + (1)/x = 5` ...(1)
Squaring both sides of (1)
`(x + 1/x)^2` = (5)2
⇒ `x^2 + (1)/x^2 + 2` = 25
⇒ `x^2 + (1)/x^2`
= 25 - 2
= 23 ...(2)
Cubing both sides of (1),
`(x + 1/x)^3` = 953
`x^3 + (1)/x^3 + 3 (x + 1/x)` = 125
⇒ `x^3 + (1)/x^3 + 3 (5)` = 125
⇒ `x^3 + (1)/x^3`
= 125 - 15
= 110
Squaring both sides of (2),
`(x^2 + 1/x^2)^2` = (23)2
⇒ `x^4 = (1)/x^4 + = 529`
⇒ `x^4 + (1)/x^4`
= 529 - 2
= 527.
APPEARS IN
संबंधित प्रश्न
Find the cube of : 5a + 3b
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
Use property to evaluate : 133 + (-8)3 + (-5)3
Use property to evaluate : 383 + (-26)3 + (-12)3
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^2 + 1/a^2 )`
If x3 + y3 = 9 and x + y = 3, find xy.
Simplify:
(a + b)3 + (a - b)3
Expand: (x + 3)3.
Expand: `((2m)/n + n/(2m))^3`.
Expand: `[x + 1/y]^3`
