Question

Find the value of
a and b if 7-√2/7+√2 =a-b√2​

Answer 1

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Answer 2

EXPLANATION

Rationalize the equation

$\large \implies{ \frac{7 - \sqrt{2} }{7 + \sqrt{2} } = a \: - b \sqrt{2} } \\ \\ \large \implies{ \frac{7 - \sqrt{2} }{7 + \sqrt{2} } \times \frac{7 - \sqrt{2} }{7 - \sqrt{2} } = a - b \sqrt{2} } \\ \\ \large \implies{ \frac{(7 - \sqrt{2}) {}^{2} }{49 - 2} } = a - b \sqrt{2} \\ \\ \large \implies{ \frac{49 + 2 - 14 \sqrt{2} }{47} } = a - b \sqrt{2} \\ \\ \large \implies{ \frac{51 - 14 \sqrt{2} }{47} } = a - b \sqrt{2} \\ \\ \large \implies \orange{ \boxed{a \: = \frac{51}{47} \: }} \\ \\ \large \implies \orange{ \boxed{b \: = \frac{14}{47} }}$