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
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{3}{x} - \frac{x}{3} \right) \left( \frac{x^2}{9} + \frac{9}{x^2} + 1 \right)\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
Find the square of 2a + b.
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Expand the following:
`(4 - 1/(3x))^3`
