Advertisements
Advertisements
प्रश्न
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Advertisements
उत्तर
`"a" + (1)/"a" = 2`
`("a" + 1/"a")^2`
= `"a"^2 + (1)/"a"^2 + 2`
⇒ (2)2 = `"a"^2 + (1)/"a"^2 + 2`
⇒ `"a"^2 + (1)/"a"^2`
= 4 - 2
= 2
`("a" + 1/"a")^3`
= `"a"^3 + (1)/"a"^3 + 3("a" + 1/"a")`
⇒ (2)3 = `"a"^3 + (1)/"a"^3 + 3(2)`
⇒ `"a"^3 + (1)/"a"^3`
= 8 - 6
= 2
`("a"^2 + 1/"a"^2)^2`
= `"a"^4 + (1)/"a"^4 + 2`
⇒ (2a)2 = `"a"^4 + (1)/"a"^4 + 2`
⇒ `"a"^4 + (1)/"a"^4`
= 4 - 2
= 2
Thus, `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
APPEARS IN
संबंधित प्रश्न
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
Use the direct method to evaluate :
(3b−1) (3b+1)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate the following without multiplying:
(103)2
Simplify:
(4x + 5y)2 + (4x - 5y)2
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
