Advertisements
Advertisements
प्रश्न
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
उत्तर
We have `x = (sqrt3 + 1)/2`
It can be simplified as
`2x - 1 = sqrt3`
On squaring both sides, we get
`(2x - 1)^2 = (sqrt3)^2`
`(2x)^2 + 1 - 2 xx 2x = 3`
`4x^2 + 1 - 4x = 3`
`4x^2 - 4x - 2 = 0`
The given equation can be rewritten as `4x^2 + 2x^2 - 8x + 7 = x(4x^2 - 4x - 2) + 3 + 7`
Therefore, we have
`4x^3 + 2x^2 - 8x + 7 = x(0) + 6/4 (0) + 3 + 4`
= 3 + 7
= 10
Hence, the value of given expression is 10
APPEARS IN
संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Rationalise the denominator of each of the following
`3/sqrt5`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(2 + sqrt3)/3`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
`root(4)root(3)(2^2)` equals to ______.
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
