If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30},$ find the value of $a$ and $b$.
If $\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30},$ find the value of $a$ and $b$.
$\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}}=a+b \sqrt{30}$
$\therefore \frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{6}} \times \frac{3 \sqrt{5}+2 \sqrt{6}}{3 \sqrt{5}+2 \sqrt{6}}=a+b \sqrt{30}$
$\therefore \frac{(2 \sqrt{6}-\sqrt{5})(3 \sqrt{5}+2 \sqrt{6})}{(3 \sqrt{5})^{2}-(2 \sqrt{6})^{2}}=a+b \sqrt{30}$
$\therefore \frac{6 \sqrt{30}+24-15-2 \sqrt{30}}{45-24}=a+b \sqrt{30}$
$\therefore \frac{9+4 \sqrt{30}}{21}=a+b \sqrt{30}$
$\therefore \frac{9}{21}+\frac{4 \sqrt{30}}{21}=a+b \sqrt{30}$
$\therefore \frac{3}{7}+\frac{4 \sqrt{30}}{21}=a+b \sqrt{30}$
Equating the coefficients of rational and irrational parts on both sides, we get $a=\frac{3}{7}$ and $b=\frac{4}{21}$
Similar Questions
Locate $\sqrt{13}$ on the number line.
Locate $\sqrt{13}$ on the number line.
If $\sqrt{2}=1.414, \sqrt{3}=1.732,$ then find the value of $\frac{4}{3 \cdot \sqrt{3}-2 \cdot \sqrt{2}}+\frac{3}{3 \cdot \sqrt{3}+2 \cdot \sqrt{2}}$
If $\sqrt{2}=1.414, \sqrt{3}=1.732,$ then find the value of $\frac{4}{3 \cdot \sqrt{3}-2 \cdot \sqrt{2}}+\frac{3}{3 \cdot \sqrt{3}+2 \cdot \sqrt{2}}$
prove that
$\frac{x^{a(b-c)}}{x^{b(a-c)}} \div\left(\frac{x^{b}}{x^{a}}\right)^{c}=1$
prove that
$\frac{x^{a(b-c)}}{x^{b(a-c)}} \div\left(\frac{x^{b}}{x^{a}}\right)^{c}=1$
Simplify the following:
$4 \sqrt{12} \times 7 \sqrt{6}$
Simplify the following:
$4 \sqrt{12} \times 7 \sqrt{6}$
State whether the following statements are true or false
Every whole number is an integer.
State whether the following statements are true or false
Every whole number is an integer.