Advertisements
Advertisements
प्रश्न
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
उत्तर
We have, `(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
For rationalising the above equation, we multiply numerator and denominator of LHS by `7 - 4sqrt(3)`, we get
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3)) = a - 6sqrt(3)`
`(5(7 - 4sqrt(3)) + 2sqrt(3)(7 - 4sqrt(3)))/(7^2 - (4sqrt(3))^2) = a - 6sqrt(3)` ...[Using identity, (a + b)(a – b) = a2 – b2]
⇒ `(35 - 20sqrt(3) + 14sqrt(3) - 24)/(49 - 48) = a - 6sqrt(3)`
⇒ `11 - 6sqrt(3) = a - 6sqrt(3) = a` = 11
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Find the value of a and b in the following:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
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)`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
