Advertisements
Advertisements
Question
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
Advertisements
Solution
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
RELATED QUESTIONS
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Find the following product:
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
If \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]
Evaluate the following without multiplying:
(95)2
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
If `49x^2 - b = (7x + 1/2)(7x - 1/2)`, then the value of b is ______.
