Question

If m=1÷2-√3 and n=1÷2+√3 then what is the value of 7m²+11mn-7n²

Answer 1

$m = \frac{1}{2 - \sqrt{3} } \\ n = \frac{1}{2 + \sqrt{3} } \\ = > m = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = > m = 2 + \sqrt{3} \\ = > n = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ = > n = 2 - \sqrt{3} \\ = > now \\ = > 7 {m}^{2} + 11mn - 2 {n}^{2} \\ = 7( {m}^{2} - {n}^{2} ) + 11mn \\ = 7(m + n)(m - n) + 11mn \\ = 7((2 + \sqrt{3} ) + (2 - \sqrt{3} ))((2 + \sqrt{3} ) - (2 - \sqrt{3} )) + 11(2 + \sqrt{3} )(2 - \sqrt{3} ) \\ = 56 \sqrt{3} + 11$
hope it helps