If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively.

1, -2

-2, 1

\(\frac{-2}{5}\), 1

2, 3/5

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mbabzy

8 years ago

Rationalize it collect like terms nd cut so i got 10-5 square root 6 divide tru by 2 den give m=-2 n=1

Tobbybello

5 years ago

Please full workings of number 3

Unixok

2 years ago

2√3 -√2
_________
√3+2√2
To solve this we start by rationalization; that is multiplying both the numerator and denominator by the conjugate of the given binomial surd (a binomial surd is a surd that is added or subtrcted from another surd or maybe number) in the denominator . when this is done, we will have this

(2√3 - √2) × (√3 - 2√2)
___________________
(√3 + 2√2) × (√3 - 2√2)

simplifying this will leave us with
-5√6 +10
___________
3 - 8

Which is then equal to

-5√6+10
_________
-5

=

√6-2
which is equal to

-2 +√6

therefore
m= -2
and
n. = +1