Advertisements
Advertisements
प्रश्न
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Advertisements
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:
`(11 + sqrt11)(11 - sqrt11)`
Rationalise the denominator of the following:
`3/(2sqrt5)`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
Classify the following number as rational or irrational:
2π
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
