Question

if 2√3+3√2/÷2√3-3√2=a+b√6 value of a, b​

Answer 1

Answer:

a= -5

b= 2

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Answer 2

Answer:

a = -5 and b = -2

Step-by-step explanation:

I think your question is $\frac{2\sqrt{3}+3\sqrt{2}}{2\sqrt{3}-3\sqrt{2}} = a+b\sqrt{6}$.

On rationalizing L.H.S., we get

$\frac{(2\sqrt{3}+3\sqrt{2})(2\sqrt{3}+3\sqrt{2})}{(2\sqrt{3}-3\sqrt{2})(2\sqrt{3}+3\sqrt{2})} = a+b\sqrt{6}$

or $\frac{(2\sqrt{3}+3\sqrt{2})^{2}}{(2\sqrt{3})^{2}-(3\sqrt{2})^{2}} = a+b\sqrt{6}$

or $\frac{12+18+12\sqrt{6}}{12-18} = a+b\sqrt{6}$

or $\frac{30+12\sqrt{6}}{-6} = a+b\sqrt{6}$

or $-5-2\sqrt{6} = a+b\sqrt{6}$

On compairing both sides, we get

a = -5 and b = -2