Question

find the values of a and b if 2√6-√5/3√5-2√6=a+b√30​

Answer 1

Answer:

the value of A is 3/7 and B is 4/21

Answer 2

Answer:

$b=4 / 21$

Step-by-step explanation:

Given$\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30}$

Rationalize the denominator with$(3 \sqrt{5}+2 \sqrt{ } 6)$

$\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}} \times \frac{3 \sqrt{5}+2 \sqrt{6}}{3 \sqrt{5}+2 \sqrt{6}}=a+b \sqrt{30}$

$\Rightarrow \frac{(2 \sqrt{6}-\sqrt{5})(3 \sqrt{5}+2 \sqrt{6})}{(3 \sqrt{5})^{2}-(2 \sqrt{6})^{2}}=a+b \sqrt{30}$

$\Rightarrow \frac{6 \sqrt{30}+24-15-2 \sqrt{30}}{45-24}=a+b \sqrt{30}$

$\Rightarrow \frac{9+4 \sqrt{30}}{21}=a+b \sqrt{30}$

$\Rightarrow \frac{9}{21}+\frac{4 \sqrt{30}}{21}=a+b \sqrt{30}$

$\Rightarrow \frac{3}{7}+\frac{4}{21}(\sqrt{30})=a+b \sqrt{30}$

Comparing both the sides, we get $a=3 / 7$ and $b=4 / 21$

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