Question

Find the value of m and n: if: (3+√2)/(3-√2) = m + n√2

Answer 1

Given :-

(3 + √2)/(3 - √2) = m + n√2

here, we've to find the value of m and n.

so first of all, we needa rationalize the denominator.

$\sf LHS :- \\ \\ \tt = \frac{3 + \sqrt{2} }{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ \\ \tt = \frac{ {(3 + \sqrt{2} )}^{2} }{(3 - \sqrt{2})(3 + \sqrt{2}) } \\ \\ \tt = \frac{(3 {})^{2} + 2(3)( \sqrt{2} ) + {( \sqrt{2}) }^{2} }{( {3})^{2} - ( { \sqrt{2} })^{2} } \\ \\ \tt = \frac{9 + 6 \sqrt{2} + 2 }{9 - 2} \\ \\ \tt = \frac{11 + 6 \sqrt{2} }{7} \\ \\ \tt = \frac{11}{7} + \frac{6}{7} \sqrt{2}$

RHS :-

= m + n√2

now comparing LHS with RHS, we get

➡ 11/7 + 6/7 √2 = m + n√2

hence, the value of :-

• m = 11/7

• n = 6/7