Question

pls do answer.... I wl mark as brainliest..​

Answer 1

QUESTION:

Rationalize the denominator : { 5√2 / (7 - 3√2) } + { 6√2 / (7 + 3√2) }

ANSWER:

• (77√2 - 6) / 31

GIVEN:

• {5√2 / (7 - 3√2)} + {6√2 / (7 + 3√2)}

TO RATIONALIZE:

• {5√2 / (7 - 3√2)} + {6√2 / (7 + 3√2)}

EXPLANATION:

Method 1:

$\sf \dashrightarrow \dfrac{ 5 \sqrt{2}}{ 7 - 3 \sqrt{2} } + \dfrac{ 6 \sqrt{2}}{7 + 3 \sqrt{2}}$

$\sf \dashrightarrow \dfrac{ 5 \sqrt{2}(7 + 3 \sqrt{2}) + 6 \sqrt{2}( 7 - 3 \sqrt{2})}{ {7}^{2} - (3 \sqrt{2 }{)}^{2} }$

$\sf \dashrightarrow \dfrac{ 35 \sqrt{2} + 15 (2) + 42 \sqrt{2} - 18(2)}{ 49 - (9(2)) }$

$\sf \dashrightarrow \dfrac{ 77 \sqrt{2} + 30 - 36}{ 49 -18 }$

$\sf \dashrightarrow \dfrac{ 77 \sqrt{2} - 6}{ 31 }$

Method 2:

$\sf Let \ A = \dfrac{ 5 \sqrt{2}}{ 7 - 3 \sqrt{2} }$

$\sf Let\ B = \dfrac{ 6 \sqrt{2}}{7 + 3 \sqrt{2}}$

Take A:

• Rationalize the denominator.

$\sf\dashrightarrow A = \dfrac{ 5 \sqrt{2}}{ 7 - 3 \sqrt{2} } \times \dfrac{7 + 3 \sqrt{2}}{7 + 3 \sqrt{2}}$

$\sf\dashrightarrow A = \dfrac{ 5 \sqrt{2}(7 + 3 \sqrt{2})}{ 7^{2} - (3 \sqrt{2} {)}^{2} }$

$\sf\dashrightarrow A = \dfrac{ 35 \sqrt{2} + 15(2) }{49 - (9 (2)) }$

$\sf \dashrightarrow A = \dfrac{ 35 \sqrt{2} + 30}{49 - 18 }$

$\sf \dashrightarrow A = \dfrac{ 35 \sqrt{2} + 30}{31 }$

Take B:

• Rationalize the denominator.

$\sf\dashrightarrow B = \dfrac{ 6 \sqrt{2}}{ 7 + 3 \sqrt{2} } \times \dfrac{7 - 3 \sqrt{2}}{7 - 3 \sqrt{2}}$

$\sf\dashrightarrow B= \dfrac{ 6 \sqrt{2}(7 - 3 \sqrt{2})}{ 7^{2} - (3 \sqrt{2} {)}^{2} }$

$\sf\dashrightarrow B= \dfrac{ 42 \sqrt{2} - 18(2)}{49 - (9(2) )}$

$\sf\dashrightarrow B= \dfrac{ 42 \sqrt{2} - 36}{49 -18}$

$\sf\dashrightarrow B= \dfrac{ 42 \sqrt{2} - 36}{31}$

$\textbf{Add A and B}$

$\sf\dashrightarrow A + B= \dfrac{ 35 \sqrt{2} + 30}{31 } + \dfrac{ 42 \sqrt{2} - 36}{31}$

$\sf\dashrightarrow A + B= \dfrac{ 77 \sqrt{2} - 6}{31 }$

$\boxed{\pink{\large{\bold{ \dfrac{ 5 \sqrt{2}}{ 7 - 3 \sqrt{2} } + \dfrac{ 6 \sqrt{2}}{7 + 3 \sqrt{2}} = \dfrac{ 77 \sqrt{2} - 6}{31 }}}}}$

Answer 2

Answer:

$answer \: is \: \frac{ \sqrt[77]{2} - 6}{31}$