Advertisements
Advertisements
प्रश्न
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Advertisements
उत्तर
(i) Consider the given equation
a2 - 3a + 1 = 0
Rewrite the given equation, we have
a2 + 1 = 3a
⇒ `[ a^2 + 1 ]/a = 3`
⇒ `[ a^2/a + 1/a ] = 3`
⇒ `[ a + 1/a ] = 3` ...(1)
(ii) We need to find `a^2 + 1/a^2`:
We know the identity, (a + b)2 = a2 + b2 + 2ab
∴ `(a + 1/a )^2 = a^2 + 1/a^2 + 2` ...(2)
From equation (1), we have,
`a + 1/a` = 3
Thus, equation (2), becomes,
⇒ `(3)^2 = a^2 + 1/a^2 + 2`
⇒ 9 = `a^2 + 1/a^2 + 2`
⇒ `a^2 + 1/a^2 = 7`
APPEARS IN
संबंधित प्रश्न
Evaluate the following product without multiplying directly:
104 × 96
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Simplify the following expressions:
`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`
If a − b = 5 and ab = 12, find the value of a2 + b2
Use identities to evaluate : (502)2
If a - b = 7 and ab = 18; find a + b.
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate :
(xy+4) (xy−4)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
