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
Expand the following, using suitable identity:
(x + 2y + 4z)2
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(x+1) (x−1)
If a - b = 10 and ab = 11; find a + b.
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Using suitable identity, evaluate the following:
1033
Simplify (2x – 5y)3 – (2x + 5y)3.
