Advertisements
Advertisements
प्रश्न
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`
Advertisements
उत्तर
Using (a + b)2 = a2 + 2ab + b2
`("a" + 1/"a")^2`
= `"a"^2 + 2"a"(1/"a") + (1/"a")^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + 2 + (1)/"a"^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + (1)/"a"^2 + 2`
⇒ `("a" + 1/"a")^2` = 14 + 2
⇒ `("a" + 1/"a")^2` = 16
⇒ `"a" + (1)/"a"` = ±4
`"a"^3 + (1)/"a"^3`
= `("a" + 1/"a")("a"^2 + 1/"a"^2 - 1)` ....[Using a3 + b3 = (a + b)(a2 + b2 - ab)]
= (±4)(14 - 1)
= (±4)(13)
= ±52.
APPEARS IN
संबंधित प्रश्न
If `( a + 1/a )^2 = 3 "and a ≠ 0; then show:" a^3 + 1/a^3 = 0`.
Use property to evaluate : 383 + (-26)3 + (-12)3
If 2x - 3y = 10 and xy = 16; find the value of 8x3 - 27y3.
Find the cube of: `"a" - (1)/"a" + "b"`
If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Simplify:
`("a" + 1/"a")^3 - ("a" - 1/"a")^3`
Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2
If `x^2 + 1/x^2` = 23, then find the value of `x + 1/x` and `x^3 + 1/x^3`
Expand (2a + 5)3
