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`
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
Write the following cube in expanded form:
`[3/2x+1]^3`
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Evaluate following using identities:
991 ☓ 1009
Evaluate of the following:
463+343
If x = −2 and y = 1, by using an identity find the value of the following
(a − b)3 + (b − c)3 + (c − a)3 =
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Evaluate the following without multiplying:
(999)2
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
