Advertisements
Advertisements
प्रश्न
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
Advertisements
उत्तर
`(3 + sqrt(7))/(3 - sqrt(7)`
= `(3 + sqrt(7))/(3 - sqrt(7)) xx (3 + sqrt(7))/(3 + sqrt(7)`
= `(3 + sqrt(7))^2/((3)^2 - (sqrt(7))^2`
= `(9 + 6sqrt(7) + 7)/(9 - 7)`
= `(16 + 6sqrt(7))/(2)`
= `8 + 3sqrt(7)`
= `"a" + "b"sqrt(7)`
Hence, a = 8 and b = 3.
APPEARS IN
संबंधित प्रश्न
Rationalize the denominator.
`1/sqrt5`
Simplify by rationalising the denominator in the following.
`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(sqrt(5) - sqrt(7))/sqrt(3)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Show that Negative of an irrational number is irrational.
Draw a line segment of length `sqrt3` cm.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
