Advertisements
Advertisements
Question
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`
Advertisements
Solution
We have, `(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
⇒ `((7 + sqrt(5))^2 - (7 - sqrt(5))^2)/((7 - sqrt(5))(7 + sqrt(5))) = a + 7/11 sqrt(5)b`
⇒ `([7^2 + (sqrt(5))^2 + 2 xx 7 xx sqrt(5)] - [7^2 + (sqrt(5))^2 - 2 xx 7 xx sqrt(5)])/(7^2 - (sqrt(5))^2) = a + 7/11 sqrt(5)b`
⇒ `(49 + 5 + 14sqrt(5) - 49 - 5 + 14sqrt(5))/(49 - 5) = a + 7/11 sqrt(5)b` ...`[("Using identity" (a + b)^2 = a^2 + 2ab + b^2),((a - b)^2 = a^2 - 2ab - b^2),("and" (a - b)(a + b) = a^2 - b^2)]`
⇒ `(28sqrt(5))/44 = a + 7/11 sqrt(5)b`
⇒ `7/11 sqrt(5) = a + 7/11 sqrt(5)b`
⇒ `0 + 7/11 sqrt(5) = a + 7/11 sqrt(5)b`
On comparing both sides, we get
a = 0 and b = 1
APPEARS IN
RELATED QUESTIONS
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
Write the rationalisation factor of \[\sqrt{5} - 2\].
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
`1/(sqrt(9) - sqrt(8))` is equal to ______.
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Simplify:
`(256)^(-(4^((-3)/2))`
