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प्रश्न
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
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उत्तर
We know that rationalization factor for `4 - 3sqrt5` is `4 + 3sqrt5`. We will multiply numerator and denominator of the given expression `(4 + 3sqrt5)/(3 - 3sqrt5)` by `4 + 3sqrt5` to get
`(4 + 3sqrt5)/(4 - 3sqrt5) xx (4 + 3sqrt5)/(4 + 3sqrt5) = ((4)^2 + (3sqrt3)^2 + 2 xx 4 xx 3sqrt5)/((4)^2 - (3sqrt5)^2)`
`= (16 + 45 + 24sqrt5)/(16 - 45)`
`= (61 + 24sqrt5)/(-29)`
`= -61/29 - 24/29 sqrt5`
On equating rational and irrational terms, we get
`a + bsqrt5 = -61/29 - 24/29 sqrt5`
Hence we get `a = -61/29, b = -24/29`
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संबंधित प्रश्न
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
Write the rationalisation factor of \[\sqrt{5} - 2\].
`root(4)root(3)(2^2)` equals to ______.
Rationalise the denominator of the following:
`2/(3sqrt(3)`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
