Question

(4√5+3√2)÷3√5-2√2=a+b√10.
find a and b​

Answer 1

Pls mark as brainliest answer

Answer 2

$\sf{\underline{\boxed{\pink{\large{♡ Question ♡}}}}}$

• if $\dfrac{ 4 \sqrt{5} + 3 \sqrt {2}}{3 \sqrt{5} - 2 \sqrt {2}} = a + b \sqrt{10}$ find a and b

$\sf{\underline{\boxed{\pink{\large{♡ Solution ♡}}}}}$

$\implies \dfrac{ 4 \sqrt{5} + 3 \sqrt {2}}{3 \sqrt{5} - 2 \sqrt {2}} = a + b \sqrt{10}$

$\implies \dfrac{ 4 \sqrt{5} + 3 \sqrt {2}}{3 \sqrt{5} - 2 \sqrt {2}} \times \dfrac{ 3\sqrt{5} + 2 \sqrt {2}}{3 \sqrt{5} + 2 \sqrt {2}} = a + b \sqrt{10}$

$\sf{\underline{\boxed{\blue{\large{\mathsf{ ( a + b ) ( a - b ) = a^2 - b^2 }}}}}}$

$\implies \dfrac{ 4\sqrt{5} (3\sqrt{5} + 2 \sqrt {2}) + 3 \sqrt {2} (3\sqrt{5} + 2 \sqrt {2}) }{ ( 3\sqrt{5})^2 - ( 2 \sqrt{2})^2} = a + b \sqrt{10}$

$\implies \dfrac{60 + 8 \sqrt{10} + 9\sqrt{10} + 12 }{ 45 - 8 } = a + b \sqrt{10}$

$\implies \dfrac{72 + 17 \sqrt{10} }{ 37 } = a + b \sqrt{10}$

• compare the terms

$\sf{\underline{\boxed{\green{\large{\mathsf{ a = \dfrac{72}{37} }}}}}}$

$\implies \dfrac{17 \sqrt{10}}{37}= b\sqrt{10}$

$\implies \dfrac{ 17}{ 37} = b \dfrac{\sqrt{10}}{\sqrt{10}}$

$\implies b = \dfrac{17}{37}$

$\sf{\underline{\boxed{\green{\large{\mathsf{ b = \dfrac{17}{37} }}}}}}$

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