Advertisements
Advertisements
प्रश्न
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
Advertisements
उत्तर
We know that,
( a + b )2 = a2 + 2ab + b2
Given that `a - 1/a` = 8 ; Substitute in equation (1), we have
`(8)^2 = a^2 + 1/a^2 - 2`
⇒ `a^2 + 1/a^2 = 64 + 2`
⇒ `a^2 + 1/a^2 = 66`
⇒ `(a + 1/a)^2 = a^2 + 1/a^2 + 2`
⇒ `(a + 1/a)^2 = 66 + 2`
⇒ `(a + 1/a)^2 = 68`
i) `a + 1/a = sqrt68 `
⇒ `sqrt(17xx4 )= _-^+2sqrt17`
ii) `a^2 - 1/a^2 = (a+1/a) (a - 1/a)`
⇒ `a^2 - 1/a^2 = _-^+2sqrt17 xx 8`
⇒ `a^2 - 1/a^2 = _-^+16sqrt17`
APPEARS IN
संबंधित प्रश्न
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Write in the expand form: `(2x - y + z)^2`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
If a + b = 7 and ab = 12, find the value of a2 + b2
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
Expand the following:
(m + 8) (m - 7)
