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1f 2√5 + 3√2/ 2√3-3√2= m+n√6 find the value of m and n​

User Beejor
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Answer:

To simplify the given expression, let's rationalize the denominator first. We have the expression:

\(\frac{2\sqrt{5} + 3\sqrt{2}}{2\sqrt{3} - 3\sqrt{2}}\)

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is \(2\sqrt{3} + 3\sqrt{2}\):

\(\frac{(2\sqrt{5} + 3\sqrt{2})(2\sqrt{3} + 3\sqrt{2})}{(2\sqrt{3} - 3\sqrt{2})(2\sqrt{3} + 3\sqrt{2})}\)

Expanding the numerator and denominator, we get:

\(\frac{4\sqrt{15} + 6\sqrt{10} + 6\sqrt{10} + 9\sqrt{4}}{4\sqrt{9} - 9\sqrt{4}}\)

Simplifying further, we have:

\(\frac{4\sqrt{15} + 12\sqrt{10} + 6 \cdot 2}{4 \cdot 3 - 9 \cdot 2}\)

\(\frac{4\sqrt{15} + 12\sqrt{10} + 12}{12 - 18}\)

\(\frac{4\sqrt{15} + 12\sqrt{10} + 12}{-6}\)

Now, we can simplify the expression and rewrite it as:

\(-\frac{2\sqrt{15} + 6\sqrt{10} + 6}{3}\)

Comparing this with \(m + n\sqrt{6}\), we can determine that \(m = -2\) and \(n = -6\). Therefore, the value of \(m\) is -2 and the value of \(n\) is -6.

User InterstellarX
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