Advertisements
Advertisements
Question
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
Solution
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
RELATED QUESTIONS
Rationalise the denominator of the following
`(3sqrt2)/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`
`(sqrt5 + 1)/sqrt2`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
Write the reciprocal of \[5 + \sqrt{2}\].
Classify the following number as rational or irrational:
`(3+sqrt23)-sqrt23`
Value of (256)0.16 × (256)0.09 is ______.
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`sqrt(2)/(2 + sqrt(2)`
